Year: 2024
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Ma, Shouhei
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4403587665