Generalized parabolic sheaves on an integral projective curve (Q1198387)

Let \(X\) be an integral projective curve defined over the complex numbers and \(D_ 1,\dots,D_ n\) mutually disjoint effective Cartier divisors on \(X\). A parabolic structure on a torsion free coherent sheaf \(E\) on \(X\) consists on a filtration of the vector space \(H^ 0(E\mid D_ j)\) for each \(j=1,\dots,n\), and on some weights associated to these filtrations allowing one to define a parabolic sheaf and the notion of (semi-)stable generalized parabolic sheaf. This technical notion occurs naturally when one studies vector bundles on singular curves by pulling them back to the desingularization of the curve. The author proves existence and studies the moduli spaces of semi-stable generalized parabolic sheaves of a certain type (for which the filtrations have only 2 steps). As an application, she obtains partial desingularizations of moduli spaces of torsion free sheaves on a nodal curve.