Derived and abelian equivalence of K3 surfaces

Huybrechts, Daniel

doi:10.1090/S1056-3911-07-00481-X

Author: Daniel Huybrechts
Journal: J. Algebraic Geom. 17 (2008), 375-400
DOI: https://doi.org/10.1090/S1056-3911-07-00481-X
Published electronically: December 6, 2007
MathSciNet review: 2369091
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Abstract | References | Additional Information

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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Additional Information

Daniel Huybrechts
Affiliation: Mathematisches Institut, Universität Bonn, Beringstr. 1, 53115 Bonn, Germany
MR Author ID: 344746
Email: huybrech@math.uni-bonn.de

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