# 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.