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arXiv · 2409.04315

Siegel operators for holomorphic differential forms

Shouhei Ma
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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.

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Shouhei Ma. 2024-09-06. Siegel operators for holomorphic differential forms. https://arxiv.org/abs/2409.04315

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