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The Intrinsic Normal Cone
 Invent. Math
, 1997
"... We suggest a construction of virtual fundamental classes of certain types of moduli spaces. Contents 0 ..."
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We suggest a construction of virtual fundamental classes of certain types of moduli spaces. Contents 0
The line bundles on the moduli of parabolic Gbundles over curves and their sections
, 1996
"... ..."
Geometric Realization of the SegalSugawara Construction, in Topology, geometry and quantum field theory
 Math. Soc. Lecture Note Ser. 308
, 2004
"... Abstract. We apply the technique of localization for vertex algebras to the SegalSugawara construction of an “internal ” action of the Virasoro algebra on affine KacMoody algebras. The result is a lifting of twisted differential operators from the moduli of curves to the moduli of curves with bund ..."
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Cited by 16 (5 self)
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Abstract. We apply the technique of localization for vertex algebras to the SegalSugawara construction of an “internal ” action of the Virasoro algebra on affine KacMoody algebras. The result is a lifting of twisted differential operators from the moduli of curves to the moduli of curves with bundles, with arbitrary decorations and complex twistings. This construction gives a uniform approach to a collection of phenomena describing the geometry of the moduli spaces of bundles over varying curves: the KZB equations and heat kernels on nonabelian theta functions, their critical level limit giving the quadratic parts of the BeilinsonDrinfeld quantization of the Hitchin system, and their infinite level limit giving a Hamiltonian description of the isomonodromy equations. 1. Introduction. 1.1. Uniformization. Let G be a complex connected simplyconnected simple algebraic group with Lie algebra g, and X a smooth projective curve over C. The geometry of G–bundles on X is intimately linked to representation theory of the affine KacMoody algebra ̂g, the universal central extension of the loop algebra Lg = g⊗K, where
Linearization of group stack actions and the Picard group of the moduli of SLr/µsbundles on a curve
, 1996
"... this technical result to determine the exact structure of Pic(MG ) where G = SL r = s (theorem 5.6). I would like to thank L. Breen to have taught me both the notion of torsor and linearization of a vector bundle in the setup of groupstack action and for his comments on a preliminary version of th ..."
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Cited by 4 (1 self)
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this technical result to determine the exact structure of Pic(MG ) where G = SL r = s (theorem 5.6). I would like to thank L. Breen to have taught me both the notion of torsor and linearization of a vector bundle in the setup of groupstack action and for his comments on a preliminary version of this paper.
On the Moduli of SL(2)bundles with Connections on P1 n fx1; : : : ; x4g
"... The moduli spaces of bundles with connections on algebraic curves have been studied from various points of view (see [6]; [10]). Our interest in this subject was motivated by its relation with the Painleve ́ equations; and also by the important role of bundles with connections in the geometric Langl ..."
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The moduli spaces of bundles with connections on algebraic curves have been studied from various points of view (see [6]; [10]). Our interest in this subject was motivated by its relation with the Painleve ́ equations; and also by the important role of bundles with connections in the geometric Langlands program [4] (for more details see the remarks at
unknown title
, 1997
"... Linearization of group stack actions and the Picard group of the moduli of SLr /µsbundles on a curve ..."
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Linearization of group stack actions and the Picard group of the moduli of SLr /µsbundles on a curve
unknown title
, 1996
"... Linearization of group stack actions and the Picard group of the moduli of SLr /µsbundles on a curve ..."
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Linearization of group stack actions and the Picard group of the moduli of SLr /µsbundles on a curve