Compositio Mathematica

Research Article

Stability and the Fourier–Mukai transform II

Kōta Yoshiokaa1

a1 Department of Mathematics, Faculty of Science, Kobe University, Kobe, 657-8501, Japan (email:


We consider the problem of preservation of stability under the Fourier–Mukai transform :D(X)→D(Y ) on an abelian surface and a K3 surface. If Y is the moduli space of μ-stable sheaves on X with respect to a polarization H, we have a canonical polarization on Y and we have a correspondence between (X,H) and . We show that the stability with respect to these polarizations is preserved under , if the degree of stable sheaves on X is sufficiently large.

(Received May 01 2007)

(Accepted June 04 2008)

2000 Mathematics Subject Classification

  • 14D20


  • moduli of stable sheaves;
  • Fourier–Mukai functor