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

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

2010-12-14

arxiv.org/abs/1012.3121v1

Mathematics

Algebraic Geometry

35 pages, 1 figure

Scientific paper

In [Ma1] S. Ma established a bijection between Fourier--Mukai partners of a K3 surface and cusps of the K\"ahler moduli space. The K\"ahler moduli space can be described as a quotient of Bridgeland's stability manifold. We study the relation between stability conditions $\sigma$ near to a cusp and the associated Fourier--Mukai partner Y in the following ways. (1) We compare the heart of $\sigma$ to the heart of coherent sheaves on Y. (2) We construct Y as moduli space of $\sigma$-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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