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arXiv · 2606.31395

Holomorphic differential forms on some orthogonal modular varieties

Shuji Horinaga·Shouhei Ma
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Abstract

We construct holomorphic differential forms of many degrees, including the minimum possible one, on the modular varieties associated to the even lattices of signature $(2, n)$ with $n\equiv 1, 3$ mod $8$ and discriminant $-2$ in the range $n\geq 25$. This is the first example of holomorphic differential forms of non-top degree on orthogonal modular varieties. The proof uses the Arthur multiplicity formula in the theory of automorphic representations.

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Shuji Horinaga, Shouhei Ma. 2026-06-30. Holomorphic differential forms on some orthogonal modular varieties. https://arxiv.org/abs/2606.31395

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