Abstract
Ma (Int J Math 20(6):727–750, 2009) 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 \({\mathcal{D}^b(X)}\) which respect the component \({Stab^{\dagger}(X)}\) of the stability manifold.
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