Vol. 15, No. 1, 2021

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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
Abstract

We construct a basis of the space S14(Sp12()) 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 𝒜6 is nonnegative.

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