Geodesic
Vector-Valued Modular Forms and the Gauss Map
Documenta mathematica, Tome 22 (2017), pp. 1063-1080.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

We use the gradients of theta functions at odd two-torsion points -- thought of as vector-valued modular forms -- to construct holomorphic differential forms on the moduli space of principally polarized abelian varieties, and to characterize the locus of decomposable abelian varieties in terms of the Gauss images of two-torsion points.
Classification : 11F46, 14K25, 14K10 
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Dalla Piazza, Francesco; Fiorentino, Alessio; Grushevsky, Samuel; Perna, Sara; Salvati Manni, Riccardo. Vector-Valued Modular Forms and the Gauss Map. Documenta mathematica, Tome 22 (2017), pp. 1063-1080. http://geodesic.mathdoc.fr/item/DOCMA_2017__22__a22/