Stability conditions on $A_n$-singularities

Details Stability conditions on $A_n$-singularities Stability conditions on $A_n$-singularities

2006-09-20

arxiv.org/abs/math/0609551v2

Journal of Differential Geometry 84 (2010) 87-126

Mathematics

Algebraic Geometry

43 pages, 3 figures. v2: many minor changes, published in J. Differential Geom.

Scientific paper

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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