The theta characteristic of a branched covering

Details The theta characteristic of a branched covering The theta characteristic of a branched covering

2003-12-09

arxiv.org/abs/math/0312186v1

Mathematics

Algebraic Geometry

22 pages, 5 figures

Scientific paper

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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