全纯浸没上的 $J$-方程与形变 Hermitian-Yang-Mills 方程
微分几何
2026-02-10 v4
摘要
本文中，我们证明：若全纯浸没的纤维和底空间上均存在 -方程的解，则其全空间上也存在 -方程的解。方法是绝热极限技术。我们也部分证明了其逆蕴含关系。更确切地说，若全空间是 -nef 的，则每个纤维都是 -nef 的。此外，若每个纤维都有 -方程的解，则底空间也是 -nef 的。进一步，我们对形变 Hermitian-Yang-Mills 方程建立了类似的现象。
引用
@article{arxiv.2208.08576,
title = {$J$-equations and deformed Hermitian-Yang-Mills equations on holomorphic submersions},
author = {Rei Murakami},
journal= {arXiv preprint arXiv:2208.08576},
year = {2026}
}
备注
Accepted version. An alternative proof of Theorem 1.4 using the $\mathcal{C}$-subsolution has been added. A section on the dHYM equation has been added, and the title has been changed accordingly. A section on examples has also been added at the end of the paper. The proof of Lemma 2.21 (Lemma 3.10 in the previous version) has been replaced with a clearer one. Other changes are minor. 35 pages