A note on Fourier-Mukai transform

Details A note on Fourier-Mukai transform A note on Fourier-Mukai transform

2001-12-24

arxiv.org/abs/math/0112267v3

Mathematics

Algebraic Geometry

19 pages, some results added

Scientific paper

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 $\mu$-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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