A note on Fourier-Mukai transform
Abstract
In this note, we consider the problem on the preservation of stability under the Fourier-Mukai transforms. We first show that the Fourier-Mukai transform on an abelian surface or a K3 surface does not always preserve the stability, even for a μ-stable vector bundle. We next provide some positive results on this problem. Finally we discuss the birational map of moduli spaces on an abelian surface.
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