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arXiv · 2109.06142

Slopes of Siegel cusp forms and geometry of compactified Kuga varieties

Flora Poon·Riccardo Salvati Manni·Gregory Sankaran
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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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Flora Poon, Riccardo Salvati Manni, Gregory Sankaran. 2021-09-13. Slopes of Siegel cusp forms and geometry of compactified Kuga varieties. https://arxiv.org/abs/2109.06142

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