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Derived and abelian equivalence of K3 surfaces

Daniel Huybrechts
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Abstract

Tom Bridgeland constructed explicit stability conditions on K3 surfaces. This paper attempts to shed more light on these particular examples, especially on the hearts of the underlying t-structures. We prove that two K3 surfaces X and X' are derived equivalent if and only if there exist complexified polarizations B+iw and B'+iw' such that the associated abelian categories A(B+iw) and A(B'+iw') are equivalent. We study in detail the minimal objects of A(B+iw) and investigate stability under Fourier-Mukai transform.

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Daniel Huybrechts. 2006-04-06. Derived and abelian equivalence of K3 surfaces. https://arxiv.org/abs/math/0604150

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