The theta characteristic of a branched covering
Algebraic Geometry
2007-05-23 v1 Group Theory
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.
Keywords
Cite
@article{arxiv.math/0312186,
title = {The theta characteristic of a branched covering},
author = {Alex Eskin and Andrei Okounkov and Rahul Pandharipande},
journal= {arXiv preprint arXiv:math/0312186},
year = {2007}
}
Comments
22 pages, 5 figures