On the geometry of the moduli spaces of semi-stable sheaves supported on plane quartics

International audienceWe decompose each moduli space of semi-stable sheaves on the complex projective plane with support of dimension one and degree four into locally closed subvarieties, each subvariety being the good or geometric quotient of a set of morphisms of locally free sheaves modulo a reductive or a non-reductive group. We find locally free resolutions of length one of all these sheaves and describe them