Siegel operators for holomorphic differential forms
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917770363404288 |
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| author | Ma, Shouhei |
| author_facet | Ma, Shouhei |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_04315 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Siegel operators for holomorphic differential forms Ma, Shouhei Algebraic Geometry Number Theory 11F46, 11F55, 11F75 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. |
| title | Siegel operators for holomorphic differential forms |
| topic | Algebraic Geometry Number Theory 11F46, 11F55, 11F75 |
| url | https://arxiv.org/abs/2409.04315 |