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Stability and the Fourier–Mukai transform II

Part of: Families, fibrations

Published online by Cambridge University Press:  01 January 2009

Kōta Yoshioka
Kōta Yoshioka*
Affiliation:
Department of Mathematics, Faculty of Science, Kobe University, Kobe, 657-8501, Japan (email: [email protected])
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Abstract

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We consider the problem of preservation of stability under the Fourier–Mukai transform ℱℰ:D(X)→D(Y ) on an abelian surface and a K3 surface. If Y is the moduli space of μ-stable sheaves on X with respect to a polarization H, we have a canonical polarization on Y and we have a correspondence between (X,H) and . We show that the stability with respect to these polarizations is preserved under ℱℰ, if the degree of stable sheaves on X is sufficiently large.

Keywords

moduli of stable sheavesFourier–Mukai functor

MSC classification

Secondary: 14D20: Algebraic moduli problems, moduli of vector bundles
Type
Research Article
Information
Compositio Mathematica , Volume 145 , Issue 1 , January 2009 , pp. 112 - 142
Copyright
Copyright © Foundation Compositio Mathematica 2009

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