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

Heinrich Hartmann

Number 36
Author Heinrich Hartmann
Project C05
Year 2010

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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