Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911



Derived and abelian equivalence of K3 surfaces

Author: Daniel Huybrechts
Journal: J. Algebraic Geom. 17 (2008), 375-400
Published electronically: December 6, 2007
MathSciNet review: 2369091
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Abstract: The paper attempts to shed more light on a particular class of stability conditions on $ K3$ surfaces constructed by Tom Bridgeland. The hearts of the underlying t-structures turn out to be significant invariants of the surface. We prove that two $ K3$ surfaces $ X$ and $ X'$ are derived equivalent if and only if there exist complexified polarizations $ B+i\omega$ and $ B'+i\omega'$ such that the associated abelian categories $ \mathcal{A}(\exp(B+i\omega))$ and $ \mathcal{K}(\exp(B'+i\omega'))$ are equivalent. We study in detail the minimal objects of $ \mathcal{A}(\exp(B+i\omega))$ and investigate stability under the Fourier-Mukai transform.

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Daniel Huybrechts
Affiliation: Mathematisches Institut, Universität Bonn, Beringstr. 1, 53115 Bonn, Germany

Received by editor(s): April 1, 2006
Received by editor(s) in revised form: January 4, 2007
Published electronically: December 6, 2007

American Mathematical Society