The line bundles on the moduli of parabolic G-bundles over curves and their sections
Identifieur interne : 002518 ( Istex/Curation ); précédent : 002517; suivant : 002519The line bundles on the moduli of parabolic G-bundles over curves and their sections
Auteurs : Yves Laszlo [France] ; Christoph Sorger [France]Source :
- Annales scientifiques de l'Ecole normale superieure [ 0012-9593 ] ; 1997.
English descriptors
- KwdEn :
- Algebra, Algebraic, Algebraic group, Analogous statement, Annales, Annales scientifiques, Base change, Basic representation, Beauville, Bore1 subgroup, Canonical, Canonical isomorphism, Central extension, Coarse moduli spaces, Cocycle, Cohomology, Conformal, Conformal blocks, Connectedness, Determinant, Determinant bundle, Determinant line bundle, Direct limit, Dominant weight, Dynkin, Dynkin index, Factorial, Faltings, Functor, Highest root, Highest weight, Homogeneous space, Injective, Irreducible, Isomorphic, Isomorphism, Kumar, Laszlo, Line bundle, Line bundles, Local sections, Modulus, Morphism, Morphisms, Mumford group, Narasimhan, Normale, Normale sup6rieure, Parabolic, Parameterized, Pfaffian, Pfaffian line bundle, Picard, Picard group, Picard groups, Projective, Pullback, Quotient, Resp, S6rie tome, Scientifiques, Simple connectedness, Simple roots, Sorger, Square root, Stacks, Standard parabolic subgroup, Standard representation, Structure group, Subgroup, Tome, Topology, Trivialization, Trivializations, Universal family, Usual cocycle condition, Vector bundles, Vector space, Verlinde formula.
- Teeft :
- Algebra, Algebraic, Algebraic group, Analogous statement, Annales, Annales scientifiques, Base change, Basic representation, Beauville, Bore1 subgroup, Canonical, Canonical isomorphism, Central extension, Coarse moduli spaces, Cocycle, Cohomology, Conformal, Conformal blocks, Connectedness, Determinant, Determinant bundle, Determinant line bundle, Direct limit, Dominant weight, Dynkin, Dynkin index, Factorial, Faltings, Functor, Highest root, Highest weight, Homogeneous space, Injective, Irreducible, Isomorphic, Isomorphism, Kumar, Laszlo, Line bundle, Line bundles, Local sections, Modulus, Morphism, Morphisms, Mumford group, Narasimhan, Normale, Normale sup6rieure, Parabolic, Parameterized, Pfaffian, Pfaffian line bundle, Picard, Picard group, Picard groups, Projective, Pullback, Quotient, Resp, S6rie tome, Scientifiques, Simple connectedness, Simple roots, Sorger, Square root, Stacks, Standard parabolic subgroup, Standard representation, Structure group, Subgroup, Tome, Topology, Trivialization, Trivializations, Universal family, Usual cocycle condition, Vector bundles, Vector space, Verlinde formula.
Abstract
Abstract: Let X be a complex, smooth, complete and connected curve and G be a complex simple and simply connected algebraic group. We compute the Picard group of the stack of quasi-parabolic G-bundles over X, describe explicitly its generators for classical G and G2 and then identify the corresponding spaces of global sections with the vacua spaces of Tsuchiya, Ueno and Yamada. The method uses the uniformization theorem which describes these stacks as double quotients of certain infinite dimensional algebraic groups. We describe also the dualizing bundle of the stack of G-bundles and show that it admits a unique square root, which we construct explicitly. If G is not simply connected, the square root depends on the choice of a theta-characteristic. These results about stacks allow to recover the Drezet-Narasimhan theorem (for the coarse moduli space) and to show an analogous statement when G = Sp2r. We prove also that the coarse moduli spaces of semi-stable SOr-bundles are not locally factorial for r ≥ 7.
Url:
DOI: 10.1016/S0012-9593(97)89929-6
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<front><div type="abstract" xml:lang="en">Abstract: Let X be a complex, smooth, complete and connected curve and G be a complex simple and simply connected algebraic group. We compute the Picard group of the stack of quasi-parabolic G-bundles over X, describe explicitly its generators for classical G and G2 and then identify the corresponding spaces of global sections with the vacua spaces of Tsuchiya, Ueno and Yamada. The method uses the uniformization theorem which describes these stacks as double quotients of certain infinite dimensional algebraic groups. We describe also the dualizing bundle of the stack of G-bundles and show that it admits a unique square root, which we construct explicitly. If G is not simply connected, the square root depends on the choice of a theta-characteristic. These results about stacks allow to recover the Drezet-Narasimhan theorem (for the coarse moduli space) and to show an analogous statement when G = Sp2r. We prove also that the coarse moduli spaces of semi-stable SOr-bundles are not locally factorial for r ≥ 7.</div>
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