奇异variety的Hodge对称性与Lefschetz定理
代数几何
2025-08-27 v3
摘要
我们证明了关于奇异variety拓扑结构和Hodge理论的新结果。普遍的主题是，来自不同视角对奇异性复杂度的具体条件与Hodge-Du Bois diamond的对称性密切相关。我们将其与有理 homology流形理论联系起来，并在具有有理奇异性的低维variety中对这些流形进行表征。
引用
@article{arxiv.2410.15638,
title = {Hodge symmetry and Lefschetz theorems for singular varieties},
author = {Sung Gi Park and Mihnea Popa},
journal= {arXiv preprint arXiv:2410.15638},
year = {2025}
}
备注
38 pages. First part of a two-paper replacement of the original submission. The content about Q-factoriality has been expanded and moved to arXiv:2508.17748. This part contains new results on rational homology manifolds and bounds for the local cohomological defect