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|Title: ||Blowing up of non-commutative smooth surfaces|
|Authors: ||VAN DEN BERGH, Michel|
|Issue Date: ||2001|
|Publisher: ||AMER MATHEMATICAL SOC|
|Citation: ||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.|
|ISI #: ||000170649800001|
|Type: ||Journal Contribution|
|Appears in Collections: ||Research publications|
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