The theta characteristic of a branched covering

Alex Eskin, Andrei Okounkov, Rahul Pandharipande

Research output: Contribution to journalArticlepeer-review

28 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)873-888
Number of pages16
JournalAdvances in Mathematics
Issue number3
Publication statusPublished - 15 Feb 2008
Externally publishedYes


  • Branched covering
  • Theta characteristic


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