Mathematics – Algebraic Geometry
Scientific paper
2010-01-27
Mathematics
Algebraic Geometry
10 pages, 10 figures
Scientific paper
In this paper, we prove Thomae's formula for a triple covering of $\bold P^1$ with arbitrary index. This formula gives a relation between theta constants, determinants of period integrals and the difference products of branch points. To specify a symplectic basis of the curve, we use the combinatorics of binary trees on $\bold P^1$. This symplectic basis behaves so well for degenerations that we obtain the absolute constant in this formula and reduce it to a special case treated in [Bershadsky-Radul], [Nakayashiki].
Matsumoto Keiji
Terasoma Tomohide
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