English

Slopes of Siegel cusp forms and geometry of compactified Kuga varieties

Algebraic Geometry 2025-07-24 v2

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.

Keywords

Cite

@article{arxiv.2109.06142,
  title  = {Slopes of Siegel cusp forms and geometry of compactified Kuga varieties},
  author = {Flora Poon and Riccardo Salvati Manni and Gregory Sankaran},
  journal= {arXiv preprint arXiv:2109.06142},
  year   = {2025}
}

Comments

Minor corrections and exposition improved following referee's report: bibliography, and affiliation of one author, updated