Please use this identifier to cite or link to this item:
http://hdl.handle.net/1942/23846Full metadata record
| DC Field | Value | Language |
|---|---|---|
| dc.contributor.advisor | VAN DEN BERGH, Michel | - |
| dc.contributor.author | PRESOTTO, Dennis | - |
| dc.date.accessioned | 2017-06-01T10:24:23Z | - |
| dc.date.available | 2017-06-01T10:24:23Z | - |
| dc.date.issued | 2017 | - |
| dc.identifier.uri | http://hdl.handle.net/1942/23846 | - |
| dc.description.sponsorship | FWO | - |
| dc.language.iso | en | - |
| dc.subject.other | del Pezzo surface; noncommutative algebra; algebraic geometry | - |
| dc.title | Noncommutative del Pezzo surfaces and related topics | - |
| dc.type | Theses and Dissertations | - |
| local.format.pages | 284 | - |
| local.bibliographicCitation.jcat | T1 | - |
| dc.description.notes | Depotnummer Koninklijke Bibliotheek Albert I: D/2017/2451/ 31 | - |
| dc.relation.references | [ACdJL] M. Artin, D. Chan, A.J. de Jong, and M. Lieblich. Terminal orders on surfaces. Manuscript available at http://www.math.lsa.umich.edu/courses/711/ordersms-num.pdf. [AD09] M. Artebani and I. Dolgachev. The Hesse pencil of plane cubic curves. L'Enseignement Math ematique. Revue Internationale. 2e S erie, 55(3- 4):235{273, 2009. [AG60] M. Auslander and O. Goldman. Maximal orders. Transactions of the American Mathematical Society, 97(1):1{24, 1960. [AM69] M.F. Atiyah and I.G. Macdonald. Introduction to commutative algebra. Addison-Wesley publishing company, 1969. [AM72] M. Artin and D. Mumford. Some elementary examples of unirational varieties which are not rational. Proceedings of the London Mathematical Society. Third Series, 25:75{95, 1972. [AOU14] T. Abdelgadir, S. Okawa, and K. Ueda. Compact moduli of noncommutative projective planes. ArXiV:1411.7770, 2014. [Art92] M. Artin. Geometry of quantum planes. In Azumaya algebras, actions, and modules (Bloomington, IN, 1990), volume 124 of Contemp. Math., pages 1{15. Amer. Math. Soc., Providence, RI, 1992. [Art97] M. Artin. Some problems on three-dimensional graded domains. In Representation Theory and Algebraic Geometry, number 238 in London Math. Soc. Lecture Note Series, pages 1{20. Cambridge University Press, 1997. [AS87] M. Artin and W.F. Schelter. Graded algebras of global dimension 3. Advances in Mathematics, 66(2):171{216, 1987. 259 [AS95] M. Artin and J.T. Sta ord. Noncommutative graded domains with quadratic growth. Inventiones Mathematicae, 122(1):231{276, 1995. [ATVdB90] M. Artin, J. Tate, and M. Van den Bergh. Some algebras associated to automorphisms of elliptic curves. In P. et al. Cartier, editor, The Grothendieck Festschrift, volume 1 of Modern Birkhuser Classics, pages 33{85. Birkhuser Boston, 1990. [ATVdB91] M. Artin, J. Tate, and M. Van den Bergh. Modules over regular algebras of dimension 3. Inventiones mathematicae, 106(1):335{388, 1991. [AVdB90] M. Artin and M. Van den Bergh. Twisted homogeneous coordinate rings. Journal of Algebra, 133(2):249{271, 1990. [AZ94] M. Artin and J. Zhang. Noncommutative projective schemes. Adv. Math., 109(2):228{287, 1994. [Bas68] H. Bass. Algebraic K-Theory. W.A.Benjamin,Inc., 1968. [BDG17] I. Burban, Y. Drozd, and V. Gavran. Minors and resolutions of noncommutative schemes. European Journal of Mathematics, 2017. [Bel17] P. Belmans. Hochschild cohomology of noncommutative planes and quadrics. arXiv:1705.06098, 2017. [BES11] J. Bia lkowski, K. Erdmann, and A. Skowro nski. Deformed preprojective algebras of generalized Dynkin type Ln: Classi cation and symmetricity. Journal of Algebra, 345(1):150 { 170, 2011. [BGL87] D. Baer, W. Geigle, and H. Lenzing. The preprojective algebra of a tame hereditary artin algebra. Communications in Algebra, 15(1-2):425{457, 1987. [BK94] W. Bichsel and M.-A. Knus. Quadratic forms with values in line bundles. In Recent advances in real algebraic geometry and quadratic forms (Berkeley, CA, 1990/1991; San Francisco, CA, 1991), volume 155 of Contemp. Math., pages 293{306. American Mathematical Society, Providence, RI, 1994. [Bl78] A. A. Be linson. Coherent sheaves on Pn and problems in linear algebra. Funktsional. Anal. i Prilozhen., 12(3):68{69, 1978. [BP94] A. Bondal and A. Polishchuk. Homological properties of associative algebras: the method of helices. Russian Acad. Sci. Izv. Math, 42(2):219{ 260, 1994. [BP17] P. Belmans and D. Presotto. Maximal orders on F1 as noncommutative surfaces with exceptional collections of length 4. arXiv:1705.06943, 2017. [BPVdB17] P. Belmans, D. Presotto, and M. Van den Bergh. Comparison of two constructions of noncommutative del Pezzo surfaces with exceptional collections of length 4. In preparation, 2017. [BR16] P. Belmans and T. Raedschelders. Noncommutative quadrics and Hilbert schemes of points. ArXiV:1605.02795, 2016. [Bra13] M. Brandenburg. Rosenberg's reconstruction theorem (after Gabber). arXiv:1310.5978, 2013. [BSW10] R. Bocklandt, T. Schedler, and M. Wemyss. Superpotentials and higher order derivations. Journal of Pure and Applied Algebra, 214(9):1501 { 1522, 2010. [BVdB98] K. Bauwens and M. Van den Bergh. Normalizing extensions of the twoveronese of a three dimensional Artin-Schelter regular algebra on two generators. Journal of Algebra, 205(2):368 { 390, 1998. [CBH98] W. Crawley-Boevey and M. P. Holland. Noncommutative deformations of Kleinian singularities. Duke Mathematical Journal, 92(3):605{635, 1998. [CC15] D. Chan and K. Chan. Rational curves and ruled orders on surfaces. Journal of Algebra, 435:52{87, 2015. [Cha00] D. Chan. Twisted multi-homogeneous coordinate rings. Journal of Al- gebra, 223(2):438 { 456, 2000. [CHTV97] A. Conca, J. Herzog, N.V. Trung, and G. Valla. Diagonal subalgebras of bigraded algebras and embeddings of blow-ups of projective spaces. American Journal of Mathematics, 119(4):859{901, 1997. [CI05] D. Chan and C. Ingalls. The minimal model program for orders over surfaces. Inventiones Mathematicae, 161(2):427{452, 2005. [CI12] D. Chan and C. Ingalls. Conic bundles and Cli ord algebras. In New trends in noncommutative algebra, Contemp. Math., pages 53{75. Amer. Math. Soc., Providence, RI, 2012. [CK03] D. Chan and R. S. Kulkarni. del Pezzo orders on projective surfaces. Advances in Mathematics, 173(1):144{177, 2003. [CN16] D. Chan and A. Nyman. Species and non-commutative P1's over nonalgebraic bimodules. Journal of Algebra, 460:143{180, 2016. [CVO93] S. Caenepeel and F. Van Oystaeyen. Quadratic forms with values in invertible modules. K-Theory. An Interdisciplinary Journal for the De- velopment, Application, and In uence of K-Theory in the Mathematical Sciences, 7(1):23{40, 1993. [DL15a] K. De Laet. Graded Cli ord algebras of prime global dimension with an action of Hp. Communications in Algebra, 43(10):4258{4282, 2015. [DL15b] K. De Laet. Quotients of degenerate Sklyanin algebras. ArXiV:1510.04024, 2015. [dNVdB04] K. de Naeghel and M. Van den Bergh. Ideal classes of three-dimensional Sklyanin algebras. Journal of Algebra, 276(2):515{551, 2004. [DR80] V. Dlab and C. M. Ringel. The preprojective algebra of a modulated graph, pages 216{231. Springer, 1980. [dTdV16] L. de Thanho er de V olcsey. On an analogue of the Markov equation for exceptional collections of length 4 . ArXiV:1607.04246, 2016. [dTdVP15] L. de Thanho er de V olcsey and D. Presotto. Homological properties of a certain noncommutative del Pezzo surface. arXiv:1503.03992v4, 2015. [dTdVP17] L. de Thanho er de V olcsey and D. Presotto. Some generalizations of preprojective algebras and their properties. Journal of algebra, 470:450{ 483, 2017. [EE05] E. Enochs and S. Estrada. Relative homological algebra in the category of quasi-coherent sheaves. Advances in Mathematics, 194(2):284{295, 2005. [EE07] P. Etingof and C. Eu. Koszulity and the Hilbert series of preprojective algebras. Math. Research Letters, 14(4):589{596, 2007. [EH] D. Eisenbud and J. Harris. Intersection theory in algebraic geometry. http://scholar.harvard.edu/ les/joeharris/ les/000- nal-3264.pdf. [Eis95] D. Eisenbud. Commutative Algebra: With a View Toward Algebraic Geometry. Graduate Texts in Mathematics. Springer, 1995. [FK16] A. Fonarev and A. Kuznetsov. Derived categories of curves as components of Fano manifolds. ArXiV:1612.02241, 2016. [Gab62] P. Gabriel. Des catégories abéliennes. Bull. Soc. Math. France, 90:323{ 448, 1962. [GD63] A. Grothendieck and J. Dieudonné. éléments de géométrie alg ebrique iii: etude cohomologique des faiscaux coherents, premiere partie (EGA 3a). Institut des Hautes Etudes Scienti ques. Publications Math ematiques, 17:91, 1963. [GD65] A. Grothendieck and J. Dieudonn e. el ements de g eom etrie alg ebrique. IV. etude locale des sch emas et des morphismes de sch emas. II (EGA 4b). Institut des Hautes Etudes Scienti ques. Publications Math ematiques, 24:231, 1965. [GP79] I.M. Gelfand and V.A. Ponomarev. Model algebras and representations of graphs. Funkc. anal. i. priloz, 13:112, 1979. [Gro71] A. Grothendieck. r^evetement etales et groupe fondamental (SGA 1), volume 224 of Lecture Notes in Mathematics. Springer, 1971. [GZ67] P. Gabriel and M. Zisman. Calculus of fractions and homotopy theory. Ergebnisse der Mathematik und ihrer Grenzgebiete. Springer-Verlag, 1967. [Har97] R. Hartshorne. Algebraic Geometry. Graduate Texts in Mathematics. Springer-Verslag, 8 edition, 1997. [Haz16] R. Hazrat. Graded rings and graded Grothendieck groups, volume 435 of London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge, 2016. [HP52] W. V. D. Hodge and D. Pedoe. Methods of algebraic geometry. Vol. II., Book IV. Cambridge, at the University Press, 1952. [KL91] G.R. Krause and T.H. Lenagan. Growth of algebras and Gelfand-Kirillov dimension. Graduate Studies in Mathematics. American Mathematical Society, 1991. [Kle80] S. L. Kleiman. Relative duality for quasicoherent sheaves. Compositio Mathematica, 41(1):39{60, 1980. [KO94] S. A. Kuleshov and D. O. Orlov. Exceptional sheaves on del Pezzo surfaces. Izv. Ross. Akad. Nauk Ser. Mat., 58(3):53{87, 1994. [KS15] A. Krug and P. Sosna. On the derived category of the Hilbert scheme of points on an Enriques surface. Selecta Mathematica. New Series, 21(4):1339{1360, 2015. [KSK+09] K. Kurano, E. Sato, Anurag K., A.K. Singh, and K. Watanabe. Multigraded rings, diagonal subalgebras, and rational singularities. Journal of Algebra, 322(9):3248 { 3267, 2009. [Kuz06] A. G. Kuznetsov. Hyperplane sections and derived categories. Izv. Ross. Akad. Nauk Ser. Mat., 70(3):23{128, 2006. [Kuz08] A.G. Kuznetsov. Derived categories of quadric brations and intersections of quadrics. Advances in Mathematics, 218(5):1340{1369, 2008. [Kuz17] A.G. Kuznetsov. Exceptional collections in surface-like categories. arXiv:1703.07812, 2017. [Lam07] T.Y. Lam. Exercises in modules and rings. Problem books in mathematics. Springer, 2007. [LB95] L. Le Bruyn. Central singularities of quantum spaces. Journal of Algebra, 177(1):142{153, 1995. [LN07] J. Lipman and A. Neeman. Quasi-perfect scheme-maps and boundedness of the twisted inverse image functor. Illinois Journal of Mathematics, 51(1):209{236, 2007. [LVdB06] W. Lowen and M. Van den Bergh. Deformation theory of abelian categories. Transactions of the American Mathematical Society, 358(12):5441{5483, 2006. [Mar79] A. Markov. Sur les formes quadratiques binaires ind e nies. Mathema- tische Annalen, 15:381{406, 1879. [Mor98] I. Mori. The center of some quantum projective planes. Journal of Algebra, 204(1):15{31, 1998. [Mor07] I. Mori. Intersection theory over quantum ruled surfaces. Journal of Pure and Applied Algebra, 211:25{41, 2007. [Nym04a] A. Nyman. Points on quantum projectivizations. Mem. Amer. Math. Soc., 167(795), 2004. [Nym04b] A. Nyman. Serre duality for noncommutative P1-bundles. Transactions of the American Mathematical Society, 357(4):1349{1416, 2004. [Nym04c] A. Nyman. Serre niteness and Serre vanishing for noncommutative P1-bundles. Journal of Algebra, 278(1):32{42, 2004. [Nym15] A. Nyman. Noncommutative Tsen's theorem in dimension one. arXiv 1408.3748, January 2015. [OF89] A. V. Odesskii and B. L Feigin. Elliptic Sklyanin algebras (in russian). Funktsional Anal. i Prilozhen., 23(3):45{54, 1989. [Oka11] S. Okawa. Semi-orthogonal decomposability of the derived category of a curve. Advances in Mathematics, 228(5):2869{2873, 2011. [Orl92] D. Orlov. Projective bundles, monoidal transformations, and derived categories of coherent sheaves. Izv. Ross. Akad. Nauk Ser. Mat., 56(4):852{ 862, 1992. [Orl15] D. Orlov. Geometric realizations of quiver algebras. Proceedings of the Steklov Institute of Mathematics, 290(1):70{83, 2015. [Orl16] D. Orlov. Smooth and proper noncommutative schemes and gluing of DG categories. Advances in Mathematics, 302:59{105, 2016. [Pol05] A. Polishchuk. Noncommutative proj and coherent algebras. Mathemat- ical Research Letters, 12(1):63{74, 2005. [Poo08] B. Poonen. Isomorphism types of commutative algebras of nite rank over an algebraically closed eld. In Computational arithmetic geome- try, volume 463 of Contemp. Math., pages 111{120. Amer. Math. Soc., Providence, RI, 2008. [Pre16] D. Presotto. Symmetric noncommutative birational transformations. arXiv:1607.08383, 2016. [Pre17] D. Presotto. Z2-algebras as noncommutative blow-ups. arXiv:1701.00413, 2017. [PVdB16] D. Presotto and M. Van den Bergh. Noncommutative versions of some classical birational transformations. Journal of Noncommutative Geom- etry, 10(1):221{244, 2016. [Rei16] M. Reid. The Du Val Singularities An, Dn, E6, E7, E8. http://homepages.warwick.ac.uk/ masda/surf/more/DuVal.pdf, August 2016. [Rin98a] C.M. Ringel. The preprojective algebra of a quiver. Canadian Mathe- matical Society Conference Proceedings, 24, 1998. [Rin98b] C.M. Ringel. The preprojective algebra of a tame quiver: The irreducible components of the module varieties. Contemporary Mathematics, 229, 1998. [Ros98] A. L. Rosenberg. The spectrum of abelian categories and reconstruction of schemes. In Rings, Hopf algebras, and Brauer groups (Antwerp/Brussels, 1996), pages 257{274. Dekker, New York, 1998. [RSS14] D. Rogalski, S.J. Sierra, and J.T. Sta ord. Noncommutative blowups of elliptic algebras. Algebras and Representation Theory, pages 1{39, 2014. [RSS15] D. Rogalski, S.J. Sierra, and J.T. Sta ord. Classifying orders in the Sklyanin algebra. Algebra & Number Theory, 9(9):2055{2119, 2015. [RSS16] D. Rogalski, S.J. Sierra, and J.T. Sta ord. Ring-theoretic blowing down: I. arXiv:1603.08128, 2016. [RVdB89] I. Reiten and M. Van den Bergh. Two-dimensional tame and maximal orders of nite representation type. Memoirs of the American Mathe- matical Society, 80(408), 1989. [Sch07] T. Schedler. Hochschild homology of preprojective algebras over the integers. arXiv:0704.3278, April 2007. [Ser55] J-P. Serre. Faisceaux algebriques coherents. Annals of Mathematics, 61(2):197{278, 1955. [Sie11] S. J. Sierra. G-algebras, twistings, and equivalences of graded categories. Algebras and Representation Theory, 14(2):377{390, 2011. [Sie14] S.J. Sierra. Talk: Ring-theoretic blowing down (joint work with Rogalski, D. and Sta ord, J.T.). Workshop Interactions between Algebraic Geometry and Noncommutative Algebra, 2014. [Skl82] E. K. Sklyanin. Some algebraic structures connected with the Yang- Baxter equation. Funct. Anal. Appl., 17:263{270, 1982. [Skl83] E. K. Sklyanin. Some algebraic structures connected with the yangbaxter equation: Representations of quantum algebras. Funct. Anal. Appl., 17:273{284, 1983. [Smi94] S. P. Smith. The four-dimensional Sklyanin algebras. In Proceedings of Conference on Algebraic Geometry and Ring Theory in honor of Michael Artin, Part I (Antwerp, 1992), volume 8, pages 65{80, 1994. [Smi96] S. P. Smith. Some nite-dimensional algebras related to elliptic curves. In Representation theory of algebras and related topics (Mexico City, 1994), volume 19 of CMS Conf. Proc., pages 315{348. Amer. Math. Soc., Providence, RI, 1996. [Smi00] S. P. Smith. Noncommutative Algebraic Geometry. lecture notes. University of Washington, 2000. [ST94] S. P. Smith and J. Tate. The center of the 3-dimensional and 4- dimensional Sklyanin algebras. In Proceedings of Conference on Algebraic Geometry and Ring Theory in honor of Michael Artin, Part I (Antwerp, 1992), volume 8, pages 19{63, 1994. [Sta78] R. P. Stanley. Hilbert functions of graded algebras. Advances in Math- ematics, 28(1):57{83, 1978. [Sta17] The Stacks Project Authors. stacks project. http://stacks.math.columbia.edu, 2017. [Ste96] D.R. Stephenson. Artin{Schelter regular algebras of global dimension three. Journal of Algebra, 183:55{73, 1996. [STV98] A. Simis, N.V. Trung, and G. Valla. The diagonal subalgebra of a blow- up algebra. Journal of Pure and Applied Algebra, 125:305328, 1998. [SV07] D. R. Stephenson and M. Vancli . Constructing Cli ord quantum P3s with nitely many points. Journal of Algebra, 312(1):86{110, 2007. [SVdB01] J. T. Sta ord and M. Van den Bergh. Noncommutative curves and non- commutative surfaces. American Mathematical Society. Bulletin. New Series, 38(2):171{216, 2001. [Tru00] N.V. Trung. Diagonal subalgebras and blow-ups of projective spaces. Vietnam Journal of Mathematics, 28(1):1{15, 2000. [TV96] J. Tate and M. Van den Bergh. Homological properties of Sklyanin al- gebras. Inventiones mathematicae, 124(1):619{647, 1996. [VdB96] M. Van den Bergh. A translation principle for the four-dimensional Sklyanin algebras. Journal of Algebra, 184(2):435 { 490, 1996. [VdB97] M. Van den Bergh. Division algebras on P2 of odd index, rami ed along a smooth elliptic curve are cyclic. In Alg ebre non commutative, groupes quantiques et invariants (Reims, 1995), volume 2 of S emin. Congr., pages 43{53. Soc. Math. France, Paris, 1997. [VdB01] M. Van den Bergh. Blowing up non-commutative smooth surfaces. Mem. Amer. Math. Soc., 154(734), 2001. [VdB11] M. Van den Bergh. Noncommutative quadrics. International Mathematics Research Notices, 2011(17):3983{4026, 2011. [VdB12] M. Van den Bergh. Noncommutative P1{bundles over commutative schemes. Trans. AMS., 364(12):6279{6313, 2012. [VdBVG84] M. Van den Bergh and J. Van Geel. A duality theorem for orders in central simple algebras over function elds. Journal of Pure and Applied Algebra, 31(1-3):227{239, 1984. [VG02] M. Van Gastel. On the center of the Proj of a three dimensional regular algebra. Communications in Algebra, 30(1):1{25, 2002. [Wal77] C. T. C. Wall. Nets of conics. Mathematical Proceedings of the Cambridge Philosophical Society, 81(3):351{364, 1977. [Wal98] C. T. C. Wall. Pencils of binary quartics. Rendiconti del Seminario Matematico della Universit a di Padova. (The Mathematical Journal of the University of Padova), 99:197{217, 1998. [Wal09] C. Walton. Degenerate Sklyanin algebras and generalized twisted homo- geneous coordinate rings. Journal of Algebra, 322(7):2508{2527, 2009. | - |
| local.type.refereed | Non-Refereed | - |
| local.type.specified | Phd thesis | - |
| item.contributor | PRESOTTO, Dennis | - |
| item.fullcitation | PRESOTTO, Dennis (2017) Noncommutative del Pezzo surfaces and related topics. | - |
| item.accessRights | Open Access | - |
| item.fulltext | With Fulltext | - |
| Appears in Collections: | PhD theses Research publications | |
Files in This Item:
| File | Description | Size | Format | |
|---|---|---|---|---|
| thesis.pdf | 4.11 MB | Adobe PDF | View/Open |
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.