Thomae formula for abelian covers of CP1

Yaacov Kopeliovich, Shaul Zemel

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


Abelian covers of CP1, with fixed Galois group A, are classified, as a first step, by a discrete set of parameters. Any such cover X, of genus g ≥ 1, say, carries a finite set of A-invariant divisors of degree g−1 on X that produce nonzero theta constants on X. We show how to define a quotient involving a power of the theta constant on X that is associated with such a divisor Δ, some polynomial in the branching values, and a fixed determinant on X that does not depend on Δ, such that the quotient is constant on the moduli space of A-covers with the given discrete parameters. This generalizes the classical formula of Thomae, as well as all of its known extensions by various authors.

Original languageAmerican English
Pages (from-to)7025-7069
Number of pages45
JournalTransactions of the American Mathematical Society
Issue number10
StatePublished - 15 Nov 2019

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© 2019 American Mathematical Society


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