Geodesic
Irregular cusps of orthogonal modular varieties
Canadian journal of mathematics, Tome 77 (2025) no. 3, pp. 739-769

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DOI

Irregular cusps of an orthogonal modular variety are cusps where the lattice for Fourier expansion is strictly smaller than the lattice of translation. The 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.
DOI : 10.4153/S0008414X24000129
Mots-clés : Irregular cusp, orthogonal modular variety, toroidal compactification, Kodaira dimension 
Ma, Shouhei. Irregular cusps of orthogonal modular varieties. Canadian journal of mathematics, Tome 77 (2025) no. 3, pp. 739-769. doi: 10.4153/S0008414X24000129
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     title = {Irregular cusps of orthogonal modular varieties},
     journal = {Canadian journal of mathematics},
     pages = {739--769},
     year = {2025},
     volume = {77},
     number = {3},
     doi = {10.4153/S0008414X24000129},
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