Three-dimensional flops and non-commutative rings
Algebraic Geometry
2007-05-23 v1 Rings and Algebras
Abstract
If Y,Z are three-dimensional smooth varieties related by a flop, then Bondal and Orlov conjectured that the derived categories of coherent sheaves on Y and Z are equivalent. This conjecture was recently proved by Bridgeland. Our aim in this paper is to give a partially new proof of Bridgeland's result using non-commutative rings. The new proof also covers some mild singular and higher dimensional situations (including the one in the recent paper by Chen: ``Flops and Equivalences of derived Categories for Threefolds with only Gorenstein Singularities'').
Cite
@article{arxiv.math/0207170,
title = {Three-dimensional flops and non-commutative rings},
author = {Michel Van den Bergh},
journal= {arXiv preprint arXiv:math/0207170},
year = {2007}
}
Comments
22 pages