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Search Results: 1 - 10 of 4967 matches for " Christoph Sorger "
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On Moduli of G-bundles over Curves for exceptional G
Christoph Sorger
Mathematics , 1997,
Abstract: Let $G$ be a simple and simply connected complex Lie group, ${\goth{g}}$ its Lie algebra. I remove the restriction ``$G$ is of classical type or $G_2$'' made on $G$ in the papers of Beauville, Laszlo and myself [L-S] and [B-L-S] on the moduli of principal G-bundles over a curve. As I will just "patch" the missing technical points, this note should be seen as an appendix to the above cited papers.
Groupe de Picard de la variét\e de modules des thêta-caracteristiques des courbes planes
Christoph Sorger
Mathematics , 1994,
Abstract: Nous calculons le groupe de Picard de l'espace des modules $\Theta_{\planp}(d)$ des th\^eta-caract\'eristiques des courbes planes (non forc\'ement lisses) de degr\'e $d$. Nous montrons que pour $d\ge 6$, le groupe de Picard de la composante paire est engendr\'e par le fibr\'e d\'eterminant ${\cal{D}}$ et l'image r\'eciproque ${\cal{L}}$, sous le morphisme support sch\'ematique, de ${\cal{O}}_{\proj}(1)$ o\`u $\proj$ est l'espace des courbes de degr\'e $d$ sur $\planp$. Pour $1\le d \le 4$, ce groupe est engendr\'e uniquement par ${\cal{L}}$, le fibr\'e d\'eterminant \'etant trivial dans ces cas. Dans le groupe $\Cl$ des diviseurs de Weil, le fibr\'e d\'eterminant admet une racine: le fibr\'e pfaffien ${\cal{P}}$. De plus, pour $d\geq 4$ pair, ${\cal{L}}$ aussi admet une racine dans $\Cl$. Si $d=5$, le fibr\'e pfaffien s'\'etend en un fibr\'e inversible et le groupe de Picard est engendr\'e par ${\cal{L}}$ et ${\cal{P}}$. On verra ainsi que la composante paire de $\Theta_{\planp}(d)$ est localement factoriel si et seulement si $d=1,2,3$ ou $d=5$. On obtient un r\'esultat analogue pour la composante impaire. Ensuite, nous \'etudions la question d'existence d'une famille universelle sur un ouvert de l'ouvert $U$ des th\^eta-caract\'eristiques dont le faisceau sous-jacent est stable. Nous montrons que pour $d$ pair une telle famille ne peut exister, tandis que pour $d$ impair une telle famille existe, pas sur $U$ entier, mais localement dans la topologie de Zariski.
A symplectic resolution for the binary tetrahedral group
Manfred Lehn,Christoph Sorger
Mathematics , 2008,
Abstract: We describe an explicit symplectic resolution for the quotient singularity arising from the four-dimensional symplectic represenation of the binary tetrahedral group.
The line bundles on the stack of parabolic $G$-bundles over curves and their sections
Yves Laszlo,Christoph Sorger
Mathematics , 1995,
Abstract: 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 its members to the conformal blocs of Tsuchiya, Ueno and Yamada. We describe the canonical sheaf on these stacks and show that they admit a unique square root, which we will construct explicitly. Finally we show how the results on the stacks apply to the coarse moduli spaces and recover (and extend) the Drezet-Narasimhan theorem. We show moreover that the coarse moduli spaces of semi-stable $SO_r$-bundles are not locally factorial for $r\geq 7$.
The cup product of the Hilbert scheme for K3 surfaces
Manfred Lehn,Christoph Sorger
Mathematics , 2000,
Abstract: To any graded Frobenius algebra A we associate a sequence of graded Frobenius algebras A^[n] in such a way that for any smooth projective surface X with trivial canonical divisor there is a canonical isomorphism of rings between (H*X)^[n] and the cohomology H*(X^[n]) of the n-th Hilbert scheme of X.
Symmetric groups and the cup product on the cohomology of Hilbert schemes
Manfred Lehn,Christoph Sorger
Mathematics , 2000,
Abstract: The integral cohomology ring of the Hilbert scheme of n-tuples on the affine plane is shown to be isomorphic to the graded ring associated to a filtration of the ring of integral class functions on the symmetric group.
La singularité de O'Grady
Manfred Lehn,Christoph Sorger
Mathematics , 2005,
Abstract: Let M be the moduli space of semistable sheaves with Mukai vector 2v on an abelian or K3 surface where v is primitive such that =2. We show that the blow-up of the reduced singular locus of M provides a symplectic resolution of singularities. This gives a direct description of O'Grady's resolutions of M\_{K3}(2,0,4) and M\_{Ab}(2,0,2).
On the monodromy of the Hitchin connection
Yves Laszlo,Christian Pauly,Christoph Sorger
Mathematics , 2010,
Abstract: For any genus g > 1 we give an example of a family of smooth complex projective curves of genus g such that the image of the monodromy representation of the Hitchin connection on the sheaf of generalized SL(2)-theta functions of level l different from 1,2,4 and 8 contains an element of infinite order.
The Picard group of the moduli of G-bundles on a curve
Arnaud Beauville,Yves Laszlo,Christoph Sorger
Mathematics , 1996,
Abstract: Let G be a complex semi-simple group, and X a compact Riemann surface. The moduli space of principal G-bundles on X, and in particular the holomorphic line bundles on this space and their global sections, play an important role in the recent applications of Conformal Field Theory to algebraic geometry. In this paper we determine the Picard group of this moduli space when G is of classical or G_2 type (we consider both the coarse moduli space and the moduli stack).
Singular symplectic moduli spaces
Dmitry Kaledin,Manfred Lehn,Christoph Sorger
Mathematics , 2005, DOI: 10.1007/s00222-005-0484-6
Abstract: Moduli spaces of semistable sheaves on a K3 or abelian surface with respect to a general ample divisor are shown to be locally factorial, with the exception of symmetric products of a K3 or abelian surface and the class of moduli spaces found by O'Grady. Consequently, since singular moduli space that do not belong to these exceptional cases have singularities in codimension $\geq4$ they do no admit projective symplectic resolutions.
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