Related papers: Factorization of generalized Theta functions revis…

Let $G$ be a simple and simply connected complex Lie group. We discuss the moduli space of holomorphic semistable principal $G$ bundles over an elliptic curve $E$. In particular we give a new proof of a theorem of Looijenga and…

We consider generalized complete intersection manifolds in the product space of projective spaces, and work out useful aspects pertaining to the cohomology of sheaves over them. First, we present and prove a vanishing theorem on the…

We prove a general vanishing theorem for the cohomology of products of symmetric and skew-symmetric powers of an ample vector bundle on a smooth complex projective variety. Special cases include an extension of classical theorems of…

We consider a complete, unbounded, hyperbolic metric space $X$ and a concave, nonzero and nondecreasing function $\omega:[0,+\infty)\to[0,+\infty)$ with $\omega(0)=0$ and study the space $\mathcal{C}_\omega(X)$ of uniformly continous…

Let $X$ be a smooth, complete and connected curve and $G$ be a simple and simply connected algebraic group over $\comp$. We calculate the Picard group of the moduli stack of quasi-parabolic $G$-bundles and identify the spaces of sections of…

Let $X$ be a general cyclic cover of $\mathbb{CP}^{1}$ ramified at $m$ points, $\lambda_1...\lambda_m.$ we define a class of non positive divisors on $X$ of degree $g-1$ supported in the pre images of the branch points on $X$, such that the…

This is an extended version of a communication made at the international conference ``Noncommutative Geometry and Physics'' held at Orsay in april 2007. In this proceeding, we make a review of some noncommutative constructions connected to…

In this expository article, we follow the work of Langer to prove the boundedness of the moduli space of semistable torsion-free sheaves over a projective variety, in any characteristic.

We construct a moduli space of slope-semistable pure sheaves, building upon previous work of Le Potier and Jun Li on torsion-free sheaves over smooth surfaces. In particular, our construction provides a compactification of the Simpson…

Moduli of vector bundles on stacky curves behave similarly to moduli of vector bundles on curves, except there are additional numerical invariants giving many different notions of stability. We apply the existence criterion for good moduli…

We generalize Luna's fundamental lemma to smooth morphisms between stacks with good moduli spaces. We also give a precise condition for when it holds for non-smooth morphisms and versions for coherent sheaves and complexes. This generalizes…

We study the spaces of twisted conformal blocks attached to a $\Gamma$-curve $\Sigma$ with marked $\Gamma$-orbits and an action of $\Gamma$ on a simple Lie algebra $\mathfrak{g}$, where $\Gamma$ is a finite group. We prove that if $\Gamma$…

We study the moduli space of stable sheaves of Euler characteristic 1, supported on curves of arithmetic genus 2 contained in a smooth quadric surface. We show that this moduli space is rational. We give a classification of the stable…

Let (S,H) be a rational algebraic surface with an ample divisor. We compute generating functions for the Hodge numbers of the moduli spaces of H-stable rank 2 sheaves on S in terms of certain theta functions for indefinite lattices that…

For any almost-simple group $G$ over an algebraically closed field $k$ of characteristic zero, we describe the automorphism group of the moduli space of semistable $G$-bundles over a connected smooth projective curve $C$ of genus at least…

We show a few basic results about moduli spaces of semistable modules over Lie algebroids. The first result shows that such moduli spaces exist for relative projective morphisms of noetherian schemes, removing some earlier constraints. The…

We give functorial moduli construction of pure parabolic sheaves, in the sense of Alvarez-Consul and A. King, using the moduli of filtered Kronecker modules we introduced in our earlier work. We also use a version of S. G. Langton's result…

Let T be a general bidegree (2,2) divisor in the product of two projective planes. Recently A.Verra proved that the existence of two conic bundle structures (c.b.s.) on T implies a new counterexample to the Torelli theorem for Prym…

We consider the moduli space of stable torsion free sheaves of any rank on a smooth projective threefold. The singularity set of a torsion free sheaf is the locus where the sheaf is not locally free. On a threefold it has dimension $\leq…

We show that the moduli space of semistable G-bundles on an elliptic curve for a reductive group G is isomorphic to a power of the elliptic curve modulo a certain Weyl group which depend on the topological type of the bundle. This…