Stability and the Fourier–Mukai transform II

Abstract

AbstractWe consider the problem of preservation of stability under the Fourier–Mukai transform ℱℰ:D(X)→D(Y) on an abelian surface and aK3 surface. IfYis the moduli space ofμ-stable sheaves onXwith respect to a polarizationH, we have a canonical polarization$\widehat {H}$onYand we have a correspondence between (X,H) and$(Y,\widehat {H})$. We show that the stability with respect to these polarizations is preserved under ℱℰ, if the degree of stable sheaves onXis sufficiently large.