Derived equivalence and Grothendieck ring of varieties: the case of K3 surfaces of degree 12 and abelian varieties

Atsushi Ito, Makoto Miura, Shinnosuke Okawa, Kazushi Ueda

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

In this paper, we discuss the problem of whether the difference [X] - [Y] of the classes of a Fourier–Mukai pair (X, Y) of smooth projective varieties in the Grothendieck ring of varieties is annihilated by some power of the class L= [A1] of the affine line. We give an affirmative answer for Fourier–Mukai pairs of very general K3 surfaces of degree 12. On the other hand, we prove that in each dimension greater than one, there exists an abelian variety such that the difference with its dual is not annihilated by any power of L, thereby giving a negative answer to the problem. We also discuss variations of the problem.

Original languageEnglish
Article number38
JournalSelecta Mathematica, New Series
Volume26
Issue number3
DOIs
Publication statusPublished - Jul 1 2020
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)
  • Physics and Astronomy(all)

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