Non-commutative crepant resolutions: scenes from categorical geometry

Details Non-commutative crepant resolutions: scenes from categorical geometry Non-commutative crepant resolutions: scenes from categorical geometry

2011-03-28

arxiv.org/abs/1103.5380v3

Mathematics

Algebraic Geometry

57 pages; final version, to appear in "Progress in Commutative Algebra: Ring Theory, Homology, and Decompositions" (Sean Sathe

Scientific paper

Non-commutative crepant resolutions are algebraic objects defined by Van den Bergh to realize an equivalence of derived categories in birational geometry. They are motivated by tilting theory, the McKay correspondence, and the minimal model program, and have applications to string theory and representation theory. In this expository article I situate Van den Bergh's definition within these contexts and describe some of the current research in the area.

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