Mathematical Research Letters

Volume 22 (2015)

Number 6

Refined blowups

Pages: 1717 – 1732

DOI: https://dx.doi.org/10.4310/MRL.2015.v22.n6.a9

Authors

D. Kaledin (Algebraic Geometry Section, Steklov Math Institute, Moscow, Russia; Laboratory of Algebraic Geometry, National Research University, Higher School of Economics, Russian Federation; and Center for Geometry and Physics, IBS, Pohang, Republic of Korea)

A. Kuznetsov (Algebraic Geometry Section, Steklov Math Institute, Moscow, Russia; The Poncelet Laboratory, Independent University of Moscow, Russia; and Laboratory of Algebraic Geometry, National Research University, Higher School of Economics, Russian Federation)

Abstract

Categorical resolution of singularities has been constructed in [KL]. It proceeds by alternating two steps of seemingly different nature. We show how to use the formalism of filtered derived categories to combine the two steps into one. This results in a certain rather natural categorical refinement of the usual blowup of an algebraic variety in a closed subscheme.

Full Text (PDF format)

Accepted 31 August 2015

Published 23 May 2016