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arXiv · 1610.02750

Monodromy of Fermat Surfaces and Modular Symbols for Fermat curves

Ozlem Ejder
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Abstract

Let $F_n$ denote the Fermat curve given by $x^n+y^n=z^n$ and let $μ_n$ denote the Galois module of $n$th roots of unity. It is known that the integral homology group $H_1(F_n,\Z)$ is a cyclic $\Z[μ_n\times μ_n]$ module. In this paper, we prove this result using modular symbols and the modular description of Fermat curves; moreover we find a basis for the integral homology group $H_1(F_n,\Z)$. We also construct a family of Fermat curves using the Fermat surface and compute its monodromy.

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Ozlem Ejder. 2018-10-01. Monodromy of Fermat Surfaces and Modular Symbols for Fermat curves. https://arxiv.org/abs/1610.02750

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