The arithmetic volume of the moduli space of abelian surfaces

Let \(\mathcal{A}_g\) denote the moduli stack of principally polarized abelian varieties of dimension \(g\). The arithmetic height, or arithmetic volume, of \(\overline{\mathcal{A}}_g\), is defined to be the arithmetic degree of the metrized Hodge bundle \(\overline{\omega}_g\) on \(\overline{\mathc...

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Bibliographic Details
Published in:arXiv.org 2022-05
Main Authors: Jung, Barbara, Anna-Maria von Pippich
Format: Article
Language:English
Subjects:
Arithmetic
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Summary:Let \(\mathcal{A}_g\) denote the moduli stack of principally polarized abelian varieties of dimension \(g\). The arithmetic height, or arithmetic volume, of \(\overline{\mathcal{A}}_g\), is defined to be the arithmetic degree of the metrized Hodge bundle \(\overline{\omega}_g\) on \(\overline{\mathcal{A}}_g\). In 1999, K\"uhn proved a formula for the arithmetic volume of \(\overline{\mathcal{A}}_1\) in terms of special values of the Riemann zeta function. In this article, we generalize his result to the case \(g=2\).
ISSN:2331-8422