Irregular cusps of orthogonal modular varieties
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2021
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866912351150669824 |
|---|---|
| author | Ma, Shouhei |
| author_facet | Ma, Shouhei |
| contents | Irregular cusp of an orthogonal modular variety is a cusp where the lattice for Fourier expansion is strictly smaller than the lattice of translation. Presence of such a cusp affects the study of pluricanonical forms on the modular variety using modular forms. We study toroidal compactification over an irregular cusp, and clarify there the cusp form criterion for the calculation of Kodaira dimension. At the same time, we show that irregular cusps do not arise frequently: besides the cases when the group is neat or contains -1, we prove that the stable orthogonal groups of most (but not all) even lattices have no irregular cusp. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2101_02950 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Irregular cusps of orthogonal modular varieties Ma, Shouhei Algebraic Geometry Number Theory 14G35, 11F55 Irregular cusp of an orthogonal modular variety is a cusp where the lattice for Fourier expansion is strictly smaller than the lattice of translation. Presence of such a cusp affects the study of pluricanonical forms on the modular variety using modular forms. We study toroidal compactification over an irregular cusp, and clarify there the cusp form criterion for the calculation of Kodaira dimension. At the same time, we show that irregular cusps do not arise frequently: besides the cases when the group is neat or contains -1, we prove that the stable orthogonal groups of most (but not all) even lattices have no irregular cusp. |
| title | Irregular cusps of orthogonal modular varieties |
| topic | Algebraic Geometry Number Theory 14G35, 11F55 |
| url | https://arxiv.org/abs/2101.02950 |