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arXiv · 2105.03449

Smoothness of non-reductive fixed point sets and cohomology of non-reductive GIT quotients

Eloise Hamilton
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Abstract

We establish a method for calculating the Poincar\'e series of moduli spaces constructed as quotients of smooth varieties by suitable non-reductive group actions; examples of such moduli spaces include moduli spaces of unstable vector or Higgs bundles on a smooth projective curve, with a Harder-Narasimhan type of length two. To do so, we first prove a result concerning the smoothness of fixed point sets for suitable non-reductive group actions on smooth varieties. This enables us to prove that quotients of smooth varieties by such non-reductive group actions, which can be constructed using Non-Reductive GIT via a sequence of blow-ups, have at worst finite quotient singularities. We conclude the paper by providing explicit formulae for the Poincar\'e series of these non-reductive GIT quotients.

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Eloise Hamilton. 2021-05-07. Smoothness of non-reductive fixed point sets and cohomology of non-reductive GIT quotients. https://arxiv.org/abs/2105.03449

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