RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
 Video Library Archive Most viewed videos Search RSS New in collection

You may need the following programs to see the files

International conference "Birational and affine geometry"
April 27, 2012 16:00, Moscow, Steklov Mathematical Institute of RAS

Categorical resolutions of singularities

A. G. Kuznetsov

Steklov Mathematical Institute, Russian Academy of Sciences
 Video records: Flash Video 2,071.8 Mb Flash Video 340.7 Mb MP4 340.7 Mb

Abstract: A categorical resolution of singularities of an algebraic variety $Y$ is a triangulated category $T$ with an adjoint pair of functors between $D(Y)$ (the derived category of quasicoherent sheaves on $Y$) and $T$, such that the composition is the identity endofunctor of $D(Y)$. If $X \to Y$ is a usual resolution, the derived category $D(X)$ with pullback and pushforward functors is a categorical resolution only if $Y$ has rational singularities. However, I will explain that even if $Y$ has nonrational singularities, still one can construct a categorical resolution of $D(Y)$ by gluing derived categories of appropriate smooth algebraic varieties. This is a work in progress, joint with Valery Lunts.