Rank Two Fourier-Mukai Transforms for K3 Surfaces

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Abstract

We study rank two locally-free Fourier–Mukai transforms on K3 surfaces and show that they come in two distinct types according to whether the determinant of a suitable twist of the kernel is positive or not. We show that a necessary and sufficient condition on the existence of Fourier–Mukai transforms of rank 2 between the derived categories of K3 surfaces XX and YY with negative twisted determinant is that YY is isomorphic to XX and there must exist a line bundle with no cohomology. We use these results to prove that all reflexive K3 surfaces (including the degenerate ones) admit Fourier–Mukai transforms.
Original languageEnglish
Pages (from-to)192-201
Number of pages10
JournalJournal of geometry and physics
Volume118
Early online date30 Jan 2017
DOIs
Publication statusPublished - Aug 2017

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