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 inRendiconti del Circolo matematico di Palermo Vol. 71; no. 1; pp. 483 - 494
Main Authors Lee, Dami, Ray, Catherine
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.04.2022
Springer Nature B.V
Subjects
Algebra
Algorithms
Analysis
Applications of Mathematics
Automorphisms
Geometry
Jacobians
Lower bounds
Mathematics
Mathematics and Statistics
Minimal surfaces
Riemann surfaces
14H37
14H40
14C34
Period matrices
Isogeny factors
Automorphisms
Endomorphisms
Curves
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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