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

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.

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harmonic theta series, Kodaira dimension, moduli space of principally polarized complex abelian varieties
Mathematical Subject Classification 2010
Primary: 14J15
Received: 29 January 2020
Revised: 9 June 2020
Accepted: 12 July 2020
Published: 1 March 2021
Moritz Dittmann
Fachbereich Mathematik
Technische Universität Darmstadt
Riccardo Salvati Manni
Dipartimento di Matematica “Guido Castelnuovo”
Università di Roma “La Sapienza”
Nils R. Scheithauer
Fachbereich Mathematik
Technische Universität Darmstadt