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Семинар по комплексному анализу (Семинар Гончара)
5 июня 2017 г. 17:00, г. Москва, МИАН, комн. 411 (ул. Губкина, 8)
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Thomae formula for Abelian covers of the Sphere
Ya. Kopeliovich University of Connecticut
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Эта страница: | 282 |
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Аннотация:
Let $f\colon X\mapsto\mathbb{CP}^{1}$ be an Abelian cover of the sphere with $A$ as a group of automorphisms and $\lambda_1,\dots,\lambda_k$ be the ramification points of the cover. In this work we construct non-special divisors supported on $f^{-1}(\lambda_k)$. We evaluate theta functions on the images of these divisors in the Jacobian of $X$ and show that up to a certain constant not dependent on $\tau$, the period of the curve, these values are polynomials in $\lambda_1,\dots,\lambda_k.$ This work generalizes the work of Thomae for Hyperelliptic curves and Bershadsky and Radul for non-singular covers. (Joint with Shaul Zemel from Hebrew University).
Язык доклада: английский
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