Birational geometry and derived categories

Abstract

This paper is based on a talk at a conference "JDG 2017: Conference on Geometry and Topology". We survey recent progress on the DK hypothesis connecting the birational geometry and the derived categories stating that the K-equivalence of smooth projective varieties should correspond to the equivalence of their derived categories, and the K-inequality to the fully faithful embedding.

24 pages

References in corpus (8)

• Derived categories of coherent sheaves
• Phases Of N=2 Theories In 1+1 Dimensions With Boundary
• Log Crepant Birational Maps and Derived Categories
• Birational cobordisms and factorization of birational maps
• Grothendieck ring of pretriangulated categories
• Motivic measures and stable birational geometry
• The class of the affine line is a zero divisor in the Grothendieck ring: via $G_2$-Grassmannians
• Derived McKay correspondence for GL(3,C)

Cited by in corpus (4)

• Birational geometry for d-critical loci and wall-crossing in Calabi-Yau 3-folds
• On nonexistence of semi-orthogonal decompositions in algebraic geometry
• Non-commutative deformations of simple objects in a category of perverse coherent sheaves
• From Ohkawa to strong generation via approximable triangulated categories -- a variation on the theme of Amnon Neeman's Nagoya lecture series