Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/22974
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dc.contributor.authorPRESOTTO, Dennis-
dc.contributor.authorVAN DEN BERGH, Michel-
dc.date.accessioned2017-01-05T08:45:36Z-
dc.date.available2017-01-05T08:45:36Z-
dc.date.issued2016-
dc.identifier.citationJournal of Noncommutative Geometry, 10(1), p. 221-244-
dc.identifier.issn1661-6952-
dc.identifier.urihttp://hdl.handle.net/1942/22974-
dc.description.abstractIn this paper we generalize some classical birational transformations to the noncommutative case. In particular we show that 3-dimensional quadratic Sklyanin algebras (noncommutative projective planes) and 3-dimensional cubic Sklyanin algebras (non-commutative quadrics) have the same function field. In the same veinwe construct an analogue of the Cremona transform for non-commutative projective planes.-
dc.description.sponsorshipThe First author was supported by a Ph.D. fellowship of the Research Foundation Flanders(FWO), the second author is a senior researcher of the FWO.-
dc.language.isoen-
dc.publisherEUROPEAN MATHEMATICAL SOC-EMS-
dc.rightsEuropean Mathematical Society-
dc.subject.otherBirational transformation-
dc.subject.otherCremona transform-
dc.subject.otherSklyanin algebras-
dc.subject.othernon-commutative surfaces-
dc.titleNoncommutative versions of some classical birational transformations-
dc.typeJournal Contribution-
dc.identifier.epage244-
dc.identifier.issue1-
dc.identifier.spage221-
dc.identifier.volume10-
local.bibliographicCitation.jcatA1-
local.publisher.placePUBLISHING HOUSE GMBH INST MATHEMATIK TECHNISCHE UNIV BERLIN STRASSE 17, JUNI 136, BERLIN 10623, GERMANY-
dc.relation.references[1] M. Artin and W.F. Schelter. Graded algebras of global dimension 3. Adv.Math, 66:171{216, 1987. [2] M. Artin, J. Tate, and M. Bergh. Modules over regular algebras of dimension 3. Inventiones mathematicae, 106(1):335{388, 1991. [3] 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. [4] M. Artin and M. Van den Bergh. Twisted homogeneous coordinate rings. Journal of Algebra, 133(2):249{271, 1990. [5] M. Artin and J.J. Zhang. Noncommutative projective schemes. Advances in Mathematics, 109(2):228 { 287, 1994. [6] A. Bondal and A. Polishchuk. Homological properties of associative algebras: the method of helices. Russian Acad. Sci. Izv. Math, 42:219{260, 1994. [7] M. Brandenburg. Rosenberg's reconstruction theorem (after gabber). arXiv:1310.5978 [math.AG], 2013. [8] D.R.Stephenson. Artin Schelter Regular algebras of global dimension three. Journal of Alge- bra, 183:55{73, 1996. [9] Edgar Enochs and Sergio Estrada. Relative homological algebra in the category of quasi- coherent sheaves. Adv. Math., 194(2):284{295, 2005. [10] Pierre Gabriel. Des cat egories ab eliennes. Bull. Soc. Math. France, 90:323{448, 1962. [11] C. Nastasescu and F. van Oystaeyen. Methods of Graded Rings, volume 1836 of Lecture Notes in Mathematics. Springer, 2004. [12] Constantin Nastasescu and F. Van Oystaeyen. Graded and ltered rings and modules. Springer, Berlin, 1979. [13] A. Polishchuk. Noncommutative proj and coherent algebras. Math. Res. Lett., 12(1):63{74, 2005. [14] D. Rogalski, S.J. Sierra, and J.T. Sta ord. Classifying orders in the Sklyanin algebra. arXiv:1308.2213, 2013. [15] D. Rogalski, S.J. Sierra, and J.T. Sta ord. Noncommutative blowups of elliptic algebras. Algebras and Representation Theory, pages 1{39, 2014. [16] 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. [17] S. J. Sierra. G-algebras, twistings, and equivalences of graded categories. Algebr. Represent. Theory, 14(2):377{390, 2011. [18] 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. [19] S. P. Smith. Non-commutative Algebraic Geometry. lecture notes. University of Washington, 2000. [20] J. T. Sta ord and M. Van den Bergh. Noncommutative curves and noncommutative surfaces. Bull. Amer. Math. Soc. (N.S.), 38(2):171{216, 2001. [21] M. Van den Bergh. A Translation Principle for the Four-Dimensional Sklyanin Algebras . Journal of Algebra, 184(2):435 { 490, 1996. [22] M. Van den Bergh. Blowing up non-commutative smooth surfaces. Mem. Amer. Math. Soc., 154(734), 2001. [23] M. Van den Bergh. Non-commutative quadrics. ArXiv e-prints, 2008.-
local.type.refereedRefereed-
local.type.specifiedArticle-
dc.identifier.doi10.4171/JNCG/232-
dc.identifier.isi000376334200006-
dc.identifier.urlwww.ems-ph.org/journals/show_abstract.php?issn=1661-6952&vol=10&iss=1&rank=6&srch=searchterm%7Cpresotto-
dc.identifier.eissn1661-6960-
local.uhasselt.internationalno-
item.validationecoom 2017-
item.fulltextWith Fulltext-
item.accessRightsOpen Access-
item.fullcitationPRESOTTO, Dennis & VAN DEN BERGH, Michel (2016) Noncommutative versions of some classical birational transformations. In: Journal of Noncommutative Geometry, 10(1), p. 221-244.-
item.contributorPRESOTTO, Dennis-
item.contributorVAN DEN BERGH, Michel-
crisitem.journal.issn1661-6952-
crisitem.journal.eissn1661-6960-
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