紧致 Calabi–Yau 锥的形变
代数几何
2025-07-18 v2 复变函数
微分几何
摘要
设 为一紧致正规 K\"ahler 空间,其典范层为秩一的自由 模,且其奇点为孤立、有理、拟齐次的。我们证明,在某拓扑假设下, 的形变障碍集中于其奇点处,部分推广了 Namikawa–Gross 的结果。我们还证明,在某假设下, 的局部平凡形变是无障碍的。
引用
@article{arxiv.2504.03243,
title = {Deformations of Compact Calabi--Yau Conifolds},
author = {Yohsuke Imagi},
journal= {arXiv preprint arXiv:2504.03243},
year = {2025}
}
备注
76 pages. I have corrected the errors in the version 1. Theorem 3.4 and Corollary 3.5 were not true as they are. There is a counterexample to Corollary 3.5 with $p=q=0,$ given by the harmonic function $r^{2-2n}.$ Also Lemma 6.5 was not really proved