Journal of Differential Geometry

D-Equivalence and K-Equivalence

Yujiro Kawamata

Abstract

Let X and Y be smooth projective varieties over ℂ. They are called D-equivalent if their derived categories of bounded complexes of coherent sheaves are equivalent as triangulated categories, and K-equivalent if they are birationally equivalent and the pull-backs of their canonical divisors to a common resolution coincide. We expect that the two equivalences coincide for birationally equivalent varieties. We shall provide a partial answer to the above problem in this paper.

Article information

Source
J. Differential Geom., Volume 61, Number 1 (2002), 147-171.

Dates
First available in Project Euclid: 20 July 2004

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1090351323

Digital Object Identifier
doi:10.4310/jdg/1090351323

Mathematical Reviews number (MathSciNet)
MR1949787

Zentralblatt MATH identifier
1056.14021

Citation

Kawamata, Yujiro. D -Equivalence and K -Equivalence. J. Differential Geom. 61 (2002), no. 1, 147--171. doi:10.4310/jdg/1090351323. https://projecteuclid.org/euclid.jdg/1090351323


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