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The quantization conjecture revisited
 Ann. of Math
"... Version: 8/5/98 ABSTRACT: I prove the following strong version of the quantization conjecture of Guillemin and Sternberg: for a reductive group action on a smooth, compact, polarized variety ( X, ℓ), the cohomologies of ℓ over the GIT quotient are equal to the invariant parts of the cohomologies ove ..."
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Cited by 18 (4 self)
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Version: 8/5/98 ABSTRACT: I prove the following strong version of the quantization conjecture of Guillemin and Sternberg: for a reductive group action on a smooth, compact, polarized variety ( X, ℓ), the cohomologies of ℓ over the GIT quotient are equal to the invariant parts of the cohomologies over X. This generalizes the theorem of [GS], which concerned the spaces of global sections, and strengthens its subsequent extensions ([M], [V]) to RiemannRoch numbers. A remarkable byproduct is the rigidity of cohomology of certain vector bundles over the GIT quotient under a small change in the defining polarization. One application is a new proof of the BorelWeilBott theorem of [T] for the moduli stack M of Gbundles over a curve, and of analogous statements for the moduli stacks and spaces of bundles with parabolic structures. Also studied are equivariant holomorphic forms and the equivariant Hodgetode Rham spectral sequences for X and its strata, whose collapse at E1 is shown. Collapse of the Hodgetode Rham sequence for M is hence deduced.
Vector bundles on curves and theta functions
, 2005
"... These notes survey the relation between the moduli spaces of vector bundles on a curve C and the spaces of (classical) theta functions on the Jacobian J of C. The connection appears when one tries to describe the moduli space Mr of rank r ..."
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Cited by 13 (0 self)
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These notes survey the relation between the moduli spaces of vector bundles on a curve C and the spaces of (classical) theta functions on the Jacobian J of C. The connection appears when one tries to describe the moduli space Mr of rank r
Twisted equivariant Ktheory with complex coefficients
, 2008
"... Using a global version of the equivariant Chern character, we describe an effective method for computing the complexified twisted equivariant Ktheory of a space ..."
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Using a global version of the equivariant Chern character, we describe an effective method for computing the complexified twisted equivariant Ktheory of a space
Twisted equivariant Ktheory with complex coefficients
, 2008
"... Using a global version of the equivariant Chern character, we describe an effective method for computing the complexified twisted equivariant Ktheory of a space ..."
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Using a global version of the equivariant Chern character, we describe an effective method for computing the complexified twisted equivariant Ktheory of a space
The Jacobian
, 812
"... ABSTRACT. We determine the splitting type of the Verlinde vector bundles in higher genus in terms of simple semihomogeneous factors. In agreement with strange duality, the simple factors are interchanged by the FourierMukai transform, and their spaces of sections are naturally dual. ..."
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ABSTRACT. We determine the splitting type of the Verlinde vector bundles in higher genus in terms of simple semihomogeneous factors. In agreement with strange duality, the simple factors are interchanged by the FourierMukai transform, and their spaces of sections are naturally dual.