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|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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