中文

Holomorphic differential forms on some orthogonal modular varieties

代数几何 2026-06-30 v1

摘要

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)(2, n) with n1,3n\equiv 1, 3 mod 88 and discriminant 2-2 in the range n25n\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.

引用

@article{arxiv.2606.31395,
  title  = {Holomorphic differential forms on some orthogonal modular varieties},
  author = {Shuji Horinaga and Shouhei Ma},
  journal= {arXiv preprint arXiv:2606.31395},
  year   = {2026}
}