Abstract
As a consequence of the formula expressing the polynomial UD (t) in terms of theta functions, we can directly relate the cross-ratios of the branch points ai to the “theta-constants” ϑ[η](0,Ω). This result goes back to Thomae: Beitrag zur bestimmung von ϑ(0,...,0) durch die Klassenmoduln algebraischer Funktionen, Crelle, 71 (1870).
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© 2007 Birkhäuser Boston
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Mumford, D. (2007). Thomae’s formula and moduli of hyperelliptic curves. In: Tata Lectures on Theta II. Modern Birkhäuser Classics. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-4578-6_9
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DOI: https://doi.org/10.1007/978-0-8176-4578-6_9
Publisher Name: Birkhäuser, Boston, MA
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