Slopes of Siegel cusp forms and geometry of compactified Kuga varieties

Flora Poon; Riccardo Salvati Manni; Gregory Sankaran

doi:10.48550/arXiv.2109.06142

Slopes of Siegel cusp forms and geometry of compactified Kuga varieties

Flora Poon, Riccardo Salvati Manni, Gregory Sankaran

Sapienza Università di Roma

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Abstract

We study the Kodaira dimension of the compactified n-fold Kuga variety over the moduli space of principally polarised abelian g-folds. We construct a suitable compactification, which we call a Namikawa compactification, and show that in most cases it has canonical singularities. We then use results about the slope of Siegel modular forms to determine the Kodaira dimension for all g>1 and n>0.

Original language	English
Journal	Algebraic Geometry
DOIs	https://doi.org/10.48550/arXiv.2109.06142
Publication status	Acceptance date - 6 Jul 2025

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abstract = "We study the Kodaira dimension of the compactified n-fold Kuga variety over the moduli space of principally polarised abelian g-folds. We construct a suitable compactification, which we call a Namikawa compactification, and show that in most cases it has canonical singularities. We then use results about the slope of Siegel modular forms to determine the Kodaira dimension for all g>1 and n>0.",

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AB - We study the Kodaira dimension of the compactified n-fold Kuga variety over the moduli space of principally polarised abelian g-folds. We construct a suitable compactification, which we call a Namikawa compactification, and show that in most cases it has canonical singularities. We then use results about the slope of Siegel modular forms to determine the Kodaira dimension for all g>1 and n>0.

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Slopes of Siegel cusp forms and geometry of compactified Kuga varieties

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