Geodesic
Vector-Valued Modular Forms and the Gauss Map
Documenta mathematica, Tome 22 (2017), pp. 1063-1080
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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.
DOI : 10.4171/dm/587
Classification : 11F46, 14K10, 14K25 
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     author = {Francesco Dalla Piazza and Alessio Fiorentino and Sara Perna and Riccardo Salvati Manni and Samuel Grushevsky},
     title = {Vector-Valued {Modular} {Forms} and the {Gauss} {Map}},
     journal = {Documenta mathematica},
     pages = {1063--1080},
     year = {2017},
     volume = {22},
     doi = {10.4171/dm/587},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/587/}
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Francesco Dalla Piazza; Alessio Fiorentino; Sara Perna; Riccardo Salvati Manni; Samuel Grushevsky. Vector-Valued Modular Forms and the Gauss Map. Documenta mathematica, Tome 22 (2017), pp. 1063-1080. doi: 10.4171/dm/587

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