Derived and abelian equivalence of K3 surfaces
By D. Huybrechts. 2006
63 citations recorded by the source corpus.
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.
Subfields: Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/2e4e4be76893998d74ce28e56db9032bd8dd6a1d
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In Geometry and Topology
- D. Huybrechts
- Max Lieblich
- Martin Olsson
- Emanuele Macrì
- D. Piyaratne
- Antony Maciocia
- P. Stellari
- Arend Bayer
Citations in the corpus
- Fourier-Mukai partners of K3 surfaces in positive characteristic (2011, methodology): “y algebraically closed field. One can see this by lifting v and h together with X using Deligne’s theorem and then specializing semistable sheaves using Langton’s theorem. Remark3.16. Usingtheresultsof[H1], onecanrestricttoworkingwithmoduli of locally free slope-stable sheaves from the start. 4. FOUR”
- Fourier-Mukai Transforms and Bridgeland Stability Conditions on Abelian Threefolds (2013, background): “See [8] for a detailed discussion on minimal objects of some abelian categories associated to Bridgeland stability conditions on a surface.”
- Lectures on K3 Surfaces (2016, background): “In [253] it has been shown that in the latter case X is in fact isomorphic to a moduli space of μ-stable(!) vector bundles(!) on Y .”