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arXiv · 1811.07007

Automorphisms of Abelian Varieties and Principal Polarizations

Dami Lee·Catherine Ray
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Abstract

The Narasimhan-Nori conjecture asks for a closed formula for the number of non-isomorphic principal polarizations of any given abelian variety. In this paper, we introduce a new algorithm that gives a lower bound on the number of non-isomorphic principal polarizations on any given abelian variety. We show, for example, that the Jacobian of the genus four underlying curve of Schoen's I-WP minimal surface has at least 9 non-isomorphic principal polarizations. We also explore the Jacobians of Klein's quartic, Fermat's quartic, Bring's curve, and more.

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Dami Lee, Catherine Ray. 2018-11-16. Automorphisms of Abelian Varieties and Principal Polarizations. https://arxiv.org/abs/1811.07007

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