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arxiv: 1106.5217 · v2 · submitted 2011-06-26 · 🧮 math.AG

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Fourier-Mukai transforms and the wall-crossing behavior for Bridgeland's stability conditions

Hiroki Minamide , Shintarou Yanagida , Kota Yoshioka
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classification 🧮 math.AG
keywords stabilitybehaviorbridgelandfourier-mukaimukaiwall-crossingabelianassociated
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Bridgeland stability condition is preserved under the Fourier-Mukai transform by its definition. We explain the relation with Gieseker stability. By studying the wall-crossing behavior, we reprove that the moduli spaces of stable sheaves on abelian surfaces are birationally equivalent, if the associated Mukai vectors are related by isometries of the Mukai lattice.

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