Equivalence classes of polarizations and moduli spaces of sheaves (Q688331)

The goal of the paper is to compare moduli spaces of rank-two vector- bundles slope-stable with respect to different polarizations. Let \(F\) be a rank-two vector-bundle on a projective variety \(X\), and assume \(F\) is \(L_ 1\)-stable and \(L_ 2\)-unstable: the author proves that the first Chern class of a destabilizing subsheaf satisfies certain properties. This leads naturally to the introduction of walls and chambers in the ample cone of \(X\): one salient feature is that if two polarizations \(L_ 1\), \(L_ 2\) belong to the same chamber, then \(L_ 1\)-stability is the same as \(L_ 2\)-stability. The author concentrates attention to the case \(\dim X = 2\).