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 compact- ification, 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.
Slopes of Siegel cusp forms and geometry of compactified Kuga varieties / Poon, F.; Salvati Manni, R.; Sankaran, G.. - In: ALGEBRAIC GEOMETRY. - ISSN 2313-1691. - 12:6(2025), pp. 823-836. [10.14231/AG-2025-024]
Slopes of Siegel cusp forms and geometry of compactified Kuga varieties
Salvati Manni R.;
2025
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 compact- ification, 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.File allegati a questo prodotto
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