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http://hdl.handle.net/1942/5065
Title: | Blowing up of non-commutative smooth surfaces | Authors: | VAN DEN BERGH, Michel | Issue Date: | 2001 | Publisher: | AMER MATHEMATICAL SOC | Source: | MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY, 154(734). p. 1-+ | Abstract: | In this paper we will think of certain abelian categories with favorable properties as non-commutative surfaces. We show that under certain conditions a point on a non-commutative surface can be blown up. This yields a new non-commutative surface which is in a certain sense birational to the original one. This construction is analogous to blowing up a Poisson surface at a point of the zero-divisor of the Poisson bracket. By blowing up less than or equal to 8 points in the elliptic quantum plane one obtains global non-commutative deformations of Del-Pezzo surfaces. For example blowing up six points yields a non-commutative cubic surface. Under a number of extra hypotheses we obtain a formula for the number of non-trivial simple objects on such noncommutative surfaces. | Keywords: | SCHELTER REGULAR ALGEBRAS; ELLIPTIC ALGEBRAS; GRADED ALGEBRAS; MODULES; DIMENSION-3; CATEGORIES | Document URI: | http://hdl.handle.net/1942/5065 | ISSN: | 0065-9266 | e-ISSN: | 1947-6221 | ISI #: | 000170649800001 | Category: | A1 | Type: | Journal Contribution |
Appears in Collections: | Research publications |
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