Kota Yoshioka
Published 2001-12-24, updated 2002-09-20Version 3
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.
Comments: 19 pages, some results added
The Mumford-Tate conjecture for the product of an abelian surface and a K3 surface
Weak Brill-Noether on Abelian Surfaces
Fourier-Mukai transform on abelian surfaces
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