English

Siegel operators for holomorphic differential forms

Algebraic Geometry 2024-09-09 v1 Number Theory

Abstract

We give a geometric interpretation of the Siegel operators for holomorphic differential forms on Siegel modular varieties. This involves extension of the differential forms over a toroidal compactification, and we show that the Siegel operator essentially describes the restriction and descent to the boundary Kuga variety via holomorphic Leray filtration. As a consequence, we obtain equivalence of various notions of "vanishing at boundary'' for holomorphic forms. We also study the case of orthogonal modular varieties.

Keywords

Cite

@article{arxiv.2409.04315,
  title  = {Siegel operators for holomorphic differential forms},
  author = {Shouhei Ma},
  journal= {arXiv preprint arXiv:2409.04315},
  year   = {2024}
}
R2 v1 2026-06-28T18:36:33.307Z