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arXiv · 1104.1782

Cubic Surfaces with Special Periods

James A. Carlson·Domingo Toledo
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Abstract

We show that the vector of period ratios of a cubic surface is rational over $Q(ω)$, where $ω= \exp(2πi/3)$ if and only if the associate abelian variety is isogeneous to a product of Fermat elliptic curves. We also show how to construct cubic surfaces from a suitable totally real quintic number field $K_0$. The ring of rational endomorphisms of the associated abelian variety is $K = K_0(ω)$.

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James A. Carlson, Domingo Toledo. 2011-10-05. Cubic Surfaces with Special Periods. https://arxiv.org/abs/1104.1782

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