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 $\mu$-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.

19 pages, some results added

References in corpus (2)

• Irreducibility of moduli spaces of vector bundles on K3 surfaces
• Projective bundles over hyperkaehler manifolds and stability of Fourier-Mukai transform

Cited by in corpus (5)

• On the monodromy of moduli spaces of sheaves on K3 surfaces II
• Projective bundles over hyperkaehler manifolds and stability of Fourier-Mukai transform
• K-theoretic Donaldson invariants via instanton counting
• Duality Spectral Sequences for Weierstrass Fibrations and Applications
• A simple proof of stability of Fourier-Mukai transform