Automorphisms of Abelian Varieties and Principal Polarizations
Algebraic Geometry
2020-07-28 v3
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.
Keywords
Cite
@article{arxiv.1811.07007,
title = {Automorphisms of Abelian Varieties and Principal Polarizations},
author = {Dami Lee and Catherine Ray},
journal= {arXiv preprint arXiv:1811.07007},
year = {2020}
}