Harmonic theta series and the Kodaira dimension of 𝒜6

Dittmann, Moritz; Salvati Manni, Riccardo; Scheithauer, Nils R.

doi:10.2140/ant.2021.15.271

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Harmonic theta series and the Kodaira dimension of $\mathcal{A}_6$

Moritz Dittmann, Riccardo Salvati Manni and Nils R. Scheithauer

Vol. 15 (2021), No. 1, 271–285

DOI: 10.2140/ant.2021.15.271

Abstract

We construct a basis of the space $S_{14} ({Sp}_{12} (ℤ))$ of Siegel cusp forms of degree $6$ and weight $14$ consisting of harmonic theta series. One of these functions has vanishing order $2$ at the boundary which implies that the Kodaira dimension of $𝒜_{6}$ is nonnegative.

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Keywords

harmonic theta series, Kodaira dimension, moduli space of principally polarized complex abelian varieties

Mathematical Subject Classification 2010

Primary: 14J15

Milestones

Received: 29 January 2020

Revised: 9 June 2020

Accepted: 12 July 2020

Published: 1 March 2021

Authors

Moritz Dittmann
Fachbereich Mathematik Technische Universität Darmstadt Darmstadt Germany

Riccardo Salvati Manni
Dipartimento di Matematica “Guido Castelnuovo” Università di Roma “La Sapienza” Roma Italy

Nils R. Scheithauer
Fachbereich Mathematik Technische Universität Darmstadt Darmstadt Germany

Vol. 15, No. 1, 2021