On the moduli spaces of semi-stable plane sheaves of dimension one and multiplicity five

Abstract

We find locally free resolutions of length one for all semi-stable sheaves supported on curves of multiplicity five in the complex projective plane. In some cases, we also find geometric descriptions of these sheaves by means of extensions. We give natural stratifications for their moduli spaces and we describe the strata as certain quotients modulo linear algebraic groups. In most cases, we give concrete descriptions of these quotients as fibre bundles.