Moduli of parabolic stable sheaves on a projective scheme
Let \(X\) be a smooth projective variety. A parabolic bundle on \(X\) consists of a pair \(f:E\to F\), where \(E\) is a locally free sheaf on \(X\), \(F\) is a torsion sheaf on \(X\) and \(f\) is surjective. There is a notion of stability of such pairs, and a moduli space of such pairs was constructed before. In this article, the author considers a more general class of parabolic sheaves. The parabolic sheaves are still pairs \(f:E\to F\). However, in this case the base scheme \(X\) can be any projective scheme, the sheaf \(E\) is only assumed to be of pure dimension \(d\) and \(f\) is still surjective. The author then introduces the stability notion for such pairs, based on the Simpson stability of sheaves of pure dimension. The author proves that there is a coarse moduli scheme for parabolic sheaves on any projective scheme.
scientific article; zbMATH DE number 1502030
scientific article