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arXiv · 1509.06425

Triviality properties of principal bundles on singular curves

Prakash Belkale·Najmuddin Fakhruddin
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Abstract

We show that principal bundles for a semisimple group on an arbitrary affine curve over an algebraically closed field are trivial, provided the order of $π_1$ of the group is invertible in the ground field, or if the curve has semi-normal singularities. Several consequences and extensions of this result (and method) are given. As an application, we realize conformal blocks bundles on moduli stacks of stable curves as push forwards of line bundles on (relative) moduli stacks of principal bundles on the universal curve.

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Prakash Belkale, Najmuddin Fakhruddin. 2017-12-09. Triviality properties of principal bundles on singular curves. https://arxiv.org/abs/1509.06425

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