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• W2160494180 abstract "A strong version of the quantization conjecture of Guillemin and Sternberg is proved. For a reductive group action on a smooth, compact, polarized variety (X, L), the cohomologies of L over the GIT quotient X//G equal the invariant part of the cohomologies over X. This generalizes the theorem of [GS] on global sections, and strengthens its subsequent extensions ([JK], [li]) to RiemannRoch numbers. Remarkable by-products are the invariance of cohomology of vector bundles over X//G under a small change in the defining polarization or under shift desingularization, as well as a new proof of Boutot's theorem. Also studied are equivariant holomorphic forms and the equivariant Hodgeto-de Rham spectral sequences for X and its strata, whose collapse is shown. One application is a new proof of the Borel-Weil-Bott theorem of [Ti] for the moduli stack of C-bundles over a curve, and of analogous statements for the moduli stacks and spaces of bundles with parabolic structures. Collapse of the Hodge-to-de Rham sequences for these stacks is also shown." @default.
• W2160494180 created "2016-06-24" @default.
• W2160494180 creator A5085784472 @default.
• W2160494180 date "2000-07-01" @default.
• W2160494180 modified "2023-10-14" @default.
• W2160494180 title "The Quantization Conjecture Revisited" @default.
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• W2160494180 doi "https://doi.org/10.2307/2661378" @default.
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