The Hilbert compactification of the universal moduli space of semistable vector bundles over smooth curves
نویسنده
چکیده
We construct the Hilbert compactification of the universal moduli space of semistable vector bundles over smooth curves. The Hilbert compactification is the GIT quotient of some open part of an appropriate Hilbert scheme of curves in a Graßmannian. It has all the properties asked for by Teixidor.
منابع مشابه
Principal Bundles on Projective Varieties and the Donaldson-uhlenbeck Compactification
Let H be a semisimple algebraic group. We prove the semistable reduction theorem for μ–semistable principal H–bundles over a smooth projective variety X defined over the field C. When X is a smooth projective surface and H is simple, we construct the algebro– geometric Donaldson–Uhlenbeck compactification of the moduli space of μ–semistable principal H–bundles with fixed characteristic classes ...
متن کاملA universal construction for moduli spaces of decorated vector bundles over curves
Let X be a smooth projective curve over the field of complex numbers, and fix a homogeneous representation ρ : GL(r)−→ GL(V). Then, one can associate to every vector bundle E of rank r over X a vector bundle Eρ with fibre V . We would like to study triples (E,L,φ) where E is a vector bundle of rank r over X , L is a line bundle over X , and φ : Eρ −→ L is a non-trivial homomorphism. This set-up...
متن کاملThe Moduli Stack of Gieseker-sl2-bundles on a Nodal Curve Ii
Let X0 be an irreducible projective nodal curve with only one singular point, and let P0 be a line bundle on X0. The moduli SUX0(r;P0) of rank r vector bundles on X0 with determinant P0 is not compact. In [A], using the technique of Kausz ([K1], [K2]), we constructed a compactification GSL2B(X0;P0) of SUX0(2;P0), and studied its structure. Surprisingly, despite its seemingly natural definition,...
متن کاملOn Frobenius-destabilized Rank-2 Vector Bundles over Curves
Let X be a smooth projective curve of genus g ≥ 2 over an algebraically closed field k of characteristic p > 0. Let MX be the moduli space of semistable rank-2 vector bundles over X with trivial determinant. The relative Frobenius map F : X → X1 induces by pull-back a rational map V : MX1 99K MX . In this paper we show the following results. (1) For any line bundle L over X , the rank-p vector ...
متن کاملPicard groups of the moduli spaces of semistable sheaves I USHA
We compute the Picard group of the moduli space U ′ of semistable vector bundles of rank n and degree d on an irreducible nodal curve Y and show that U ′ is locally factorial. We determine the canonical line bundles of U ′ and U ′ L, the subvariety consisting of vector bundles with a fixed determinant. For rank 2, we compute the Picard group of other strata in the compactification of U ′.
متن کامل