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Stability conditions on $A_n$-singularities

Akira Ishii·Kazushi Ueda·Hokuto Uehara
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Abstract

We study the spaces of locally-finite stability conditions on the derived categories of coherent sheaves on the minimal resolutions of $A_n$-singularities supported at the exceptional sets. Our main theorem is that they are connected and simply-connected. The proof is based on the study of spherical objects in math.AG/0409151 and the homological mirror symmetry for $A_n$-singularities.

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Akira Ishii, Kazushi Ueda, Hokuto Uehara. 2006-09-20. Stability conditions on $A_n$-singularities. https://arxiv.org/abs/math/0609551

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