A note on Fourier-Mukai transform

2001/12/24 by Kōta Yoshioka, Kota Yoshioka, Yoshioka, Kota · 3 citations
Mathematics · #14D20 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #math.AG #msc:14D20

paper · pdf · doi:10.48550/arxiv.math/0112267

19 pages, some results added

openalex publication_date 2001/12/24 · arxiv created 2002/09/20 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

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

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