曲面与三维簇上 $1$-叶状结构奇点的解消
代数几何
2025-08-12 v2
摘要
我们考虑正特征下维数至多为三的簇上 -叶状结构的奇点解消。我们证明，如果允许以驯正则 Deligne--Mumford 叠作为底层空间，这类奇点可以被完全解消。如果限制在底层簇上，我们证明 -叶状结构奇点可以被简化为乘性奇点。
引用
@article{arxiv.2405.05735,
title = {Resolution of $1$-foliations singularities on surfaces and threefolds},
author = {Quentin Posva},
journal= {arXiv preprint arXiv:2405.05735},
year = {2025}
}
备注
v2: 40 pages, comments welcome. The discussion of foliations on DM stacks has been improved; the resolution on surfaces has been upgraded to a functorial statement; an appendix on Cossart's work on normal forms has been added