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DC Field | Value | Language |
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dc.contributor.author | DE THANHOFFER DE VOLCSEY, Louis | - |
dc.contributor.author | PRESOTTO, Dennis | - |
dc.date.accessioned | 2015-04-09T12:12:29Z | - |
dc.date.available | 2015-04-09T12:12:29Z | - |
dc.date.issued | 2015 | - |
dc.identifier.uri | http://hdl.handle.net/1942/18627 | - |
dc.description.abstract | Recently, de Thanhoffer de Volcsey and Van den Bergh showed that Grothendieck groups of "noncommutative Del Pezzo surfaces" with an exceptional sequence of length 4 are isomorphic to one of three types, the third one not coming from a commutative Del Pezzo surface. In this paper, we adapt the theory of noncommutative P1-bundles as appearing in the work of Van den Bergh and Nyman to produce a sheaf Z-algebra whose associated Proj has an exceptional sequence of length 4 for which the Gram matrix is of this third type. We show that this noncommutative scheme is noetherian and describe its local structure through the use of our generalized preprojective algebras. | - |
dc.language.iso | en | - |
dc.rights | arXiv.org perpetual, non-exclusive license to distribute this article | - |
dc.subject.other | Del Pezzo surface; P1-bundles; noncommutative geometry | - |
dc.title | Homological properties of a certain noncommutative Del Pezzo surface | - |
dc.type | Preprint | - |
local.format.pages | 33 | - |
local.bibliographicCitation.jcat | O | - |
dc.relation.references | [1] M. Artin and J. Zhang. Noncommutative projective schemes. Adv. Math., 109(2):228–287, 1994. [2] L. de Thanhoffer de Volcsey and M. Van den Bergh. Numerical classification of exceptional collections of length 4 on del pezzo surfaces. in preparation. [3] L. de Thanhoffer de Volcsey and D. Presotto. Some generalizations of Preprojective algebras and their properties. November 2014. arXiv 1412.6899. [4] R. Hartshorne. Algebraic Geometry. Graduate Texts in Mathematics. Springer-Verslag, 8 edition, 1997. [5] Izuru Mori. Intersection theory over quantum ruled surfaces. Journal of Pure a, 211:25–41, nd Applied Algebra. [6] A. Nyman. Serre duality for noncommutative P 1 -bundles. Trans. AMS., 357(4):1349–1416, 2004. [7] A. Nyman. Serre finiteness and serre vanishing for noncommutative P 1 -bundles. Journal of Algebra, 278(1):32–42, 2004. [8] Paul Smith. Noncommutative algebraic geometry. 1999. [9] M. Van den Bergh. Noncommutative P 1 bundles over commutative schemes. Trans. AMS., 364(12):6279–6313, 2012. | - |
local.type.specified | Preprint | - |
dc.identifier.url | http://arxiv.org/abs/1503.03992 | - |
item.accessRights | Open Access | - |
item.fullcitation | DE THANHOFFER DE VOLCSEY, Louis & PRESOTTO, Dennis (2015) Homological properties of a certain noncommutative Del Pezzo surface. | - |
item.fulltext | With Fulltext | - |
item.contributor | DE THANHOFFER DE VOLCSEY, Louis | - |
item.contributor | PRESOTTO, Dennis | - |
Appears in Collections: | Research publications |
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1503.03992v2.pdf | Non Peer-reviewed author version | 364.21 kB | Adobe PDF | View/Open |
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