Please use this identifier to cite or link to this item: 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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