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arXiv · 1012.3121

Cusps of the Kähler moduli space and stability conditions on K3 surfaces

Heinrich Hartmann
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Abstract

In [Ma1] S. Ma established a bijection between Fourier--Mukai partners of a K3 surface and cusps of the Kähler moduli space. The Kähler moduli space can be described as a quotient of Bridgeland's stability manifold. We study the relation between stability conditions $σ$ near to a cusp and the associated Fourier--Mukai partner Y in the following ways. (1) We compare the heart of $σ$ to the heart of coherent sheaves on Y. (2) We construct Y as moduli space of $σ$-stable objects. An appendix is devoted to the group of auto-equivalences of the derived category which respect the component $Stab^\dagger(X)$ of the stability manifold.

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Heinrich Hartmann. 2010-12-14. Cusps of the Kähler moduli space and stability conditions on K3 surfaces. https://doi.org/10.1007/s00208-011-0719-3

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