I will discuss recent work, with Prakash Belkale, where we show the section ring for the pair (Bun, D) is finitely generated, for D the determinant of cohomology line bundle on the stack Bun=Bun_{SL(r)}(C) parameterizing principal SL(r)-bundles on a singular stable curve C. While the result is independent of vector bundles of conformal blocks defined on the moduli space of stable curves, I’ll discuss a few applications to these bundles.
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