Projective moduli space of semistable principal sheaves for a reductive group

Let X be a smooth projective complex variety, and let G be an algebraic reductive complex group. We define the notion of principal G-sheaf, that generalises the notion of principal G-bundle. Then we define a notion of semistability, and construct the projective moduli space of semistable principal G-sheaves on X. This is a natural compactification of the moduli space of principal G-bundles. This is the announcement note presented by the second author in the conference held at Catania (11-13 April 2001), dedicated to the 60th birthday of Silvio Greco. Detailed proofs will appear elsewhere.Comment: 10 pages, LaTeX2e. Submitted to the conference proceedings of "Commutative Algebra and Algebraic Geometry", Catania, April 200

Torelli theorem for the parabolic Deligne-Hitchin moduli space

We prove that, given the isomorphism class of the parabolic Deligne-Hitchin moduli space over a smooth projective curve, we can recover the isomorphism class of the curve and the parabolic points.Comment: 20 page