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.
Cite
@article{arxiv.2409.04315,
title = {Siegel operators for holomorphic differential forms},
author = {Shouhei Ma},
journal= {arXiv preprint arXiv:2409.04315},
year = {2024}
}