Automorphisms of abelian varieties and principal polarizations

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. W...

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Bibliographic Details
Published in:Rendiconti del Circolo matematico di Palermo 2022-04, Vol.71 (1), p.483-494
Main Authors: Lee, Dami, Ray, Catherine
Format: Article
Language:English
Subjects:
Algebra
Algorithms
Analysis
Applications of Mathematics
Automorphisms
Geometry
Jacobians
Lower bounds
Mathematics
Mathematics and Statistics
Minimal surfaces
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Summary: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.
ISSN:0009-725X
1973-4409
DOI:10.1007/s12215-020-00590-7