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The theta characteristic of a branched covering

Alex Eskin·Andrei Okounkov·Rahul Pandharipande
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Abstract

We give a group-theoretic description of the parity of a pull-back of a theta characteristic under a branched covering. It involves lifting monodromy of the covering to the semidirect product of the symmetric and Clifford groups, known as the Sergeev group. As an application, we enumerate torus coverings with respect to their ramification and parity and, in particular, show that the corresponding all-degree generating functions are quasimodular forms.

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Alex Eskin, Andrei Okounkov, Rahul Pandharipande. 2003-12-09. The theta characteristic of a branched covering. https://arxiv.org/abs/math/0312186

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