Derived equivalences of Abelian varieties and symplectic isomorphisms

We study derived equivalences of Abelian varieties in terms of their associated symplectic data. For simple Abelian varieties over an algebraically closed field of characteristic zero we prove that the natural correspondence introduced by Orlov, which maps equivalences to symplectic isomorphisms, is...

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Bibliographic Details
Published inJournal of geometry and physics Vol. 122; pp. 92 - 102
Main Authors López Martín, Ana Cristina, Tejero Prieto, Carlos
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.12.2017
Subjects
Abelian variety
Fourier–Mukai transforms
Integral functors
Semihomogeneous sheaf
Symplectic isomorphism
secondary
Fourier–Mukai transforms
Integral functors
Abelian variety
Symplectic isomorphism
primary
Semihomogeneous sheaf
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Summary:We study derived equivalences of Abelian varieties in terms of their associated symplectic data. For simple Abelian varieties over an algebraically closed field of characteristic zero we prove that the natural correspondence introduced by Orlov, which maps equivalences to symplectic isomorphisms, is surjective.
ISSN:0393-0440
1879-1662
DOI:10.1016/j.geomphys.2017.01.010