The quantization conjecture revisited

  title={The quantization conjecture revisited},
  author={Constantin Teleman},
  journal={Annals of Mathematics},
  • C. Teleman
  • Published 1998
  • Mathematics
  • Annals of Mathematics
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… Expand
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