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arXiv:1012.3121math.AG

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.

arXiv comments
35 pages, 1 figure
Journal reference
Mathematische Annalen (2012) Volume 354, Issue 1, pp 1-42
DOI
doi:10.1007/s00208-011-0719-3
Subjects
math.AGAlgebraic Geometry

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  1. Category Theory for Programmers (2014) [pdf] 1 comment

    • Yeah exactly. I am interested in practical applications for programmers. I know a thing or two about the prevalance of categories in Mathematics (https://arxiv.org/abs/1012.3121). I heared many people talk about Haskell, Monads and Types <=> Proof duality, but I never heard…

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