Moduli of generalized syzygy bundles

Given a vector bundle F on a variety X and W ⊂ H0 (F) such that the evaluation map W ⊗ OX → F is surjective, its kernel SF,W is called generalized syzygy bundle. Under mild assumptions, we construct a moduli space GU0 of simple generalized syzygy bundles, and show that the natural morphism α to the moduli of simple sheaves is a locally closed embedding. If moreover H1 (X, OX) = 0, we find an explicit open subspace GV0 ofG0U where the restriction of α is an open embedding. In particular, if dim X ≥ 3 and H1 (OX) = 0, starting from an ample line bundle (or a simple rigid vector bundle) on X we construct recursively open subspaces CimBqU0ia0o2DqlZ9adWFlL0+YRFa+of moduli spaces of simple sheaves on X that are smooth, rational, quasiprojective varieties.