On finite generation of the section ring of the determinant of cohomology line bundle

Belkale, P.; Gibney, A.

doi:10.1090/tran/7564

On finite generation of the section ring of the determinant of cohomology line bundle
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Abstract:

For $C$ a stable curve of arithmetic genus $g\ge 2$ and $\mathcal {D}$ the determinant of cohomology line bundle on Bun${}_{\textrm {SL}(r)}(C)$, we show that the section ring for the pair $(\textrm {Bun}_{\textrm {SL}(r)}(C), \mathcal {D})$ is finitely generated. Applications involving vector bundles of conformal blocks are given, including quasi polynomiality at the level of the Chern character of the bundles on $\overline {M}_g$.

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