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arXiv:math/0609551 [math.AG]AbstractReferencesReviewsResources

Stability conditions on $A_n$-singularities

Akira Ishii, Kazushi Ueda, Hokuto Uehara

Published 2006-09-20, updated 2010-04-19Version 2

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.

Comments: 43 pages, 3 figures. v2: many minor changes, published in J. Differential Geom.
Journal: Journal of Differential Geometry 84 (2010) 87-126
Categories: math.AG, math.SG
Subjects: 14J17, 14J32, 18E30
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