#### 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 ${S}_{14}\left({Sp}_{12}\left(ℤ\right)\right)$ 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 ${\mathsc{𝒜}}_{6}$ is nonnegative.

##### Keywords
harmonic theta series, Kodaira dimension, moduli space of principally polarized complex abelian varieties
Primary: 14J15