AI 中文总结
研究构造光滑复射影簇，一种基于特定同调纤维丛，另一种基于有理上同调环面，通过这两种构造反驳了科奇克猜想、博瓦迪利亚 - 科拉尔猜想剩余蕴含关系及第一作者的一个猜想。
AI 中文摘要
我们构造了一个光滑复射影簇，其阿尔巴内塞态射是同伦纤维丛但不是淹没映射。该簇在圆上有光滑纤维化，尽管其上每个全纯一阶形式都有零点。第二种构造产生了光滑复射影簇\(X\)，使得\(X\)的每个连通有限平展覆盖上每个非零全纯一阶形式的青本复形是正合的，而\(X\)不存在无零点的实闭一阶形式。这两种构造分别基于科雷亚 - 科拉尔的一个不是同伦纤维丛的同调纤维丛以及德巴雷 - 江 - 拉霍兹构造的有理上同调环面。因此，我们反驳了科奇克猜想、博瓦迪利亚 - 科拉尔猜想中剩下的蕴含关系以及第一作者的一个猜想。
英文摘要
We construct a smooth complex projective variety whose Albanese morphism is a homotopy fiber bundle but not a submersion. The same variety fibers smoothly over the circle, although every holomorphic one-form on it has a zero. A second construction yields smooth complex projective varieties $X$ such that the Aomoto complex of every nonzero holomorphic one-form on every connected finite étale cover of $X$ is exact, while $X$ admits no real closed one-form without zeros. The two constructions build, respectively, on a homology fiber bundle of Corrêa--Kollár that is not a homotopy fiber bundle and on a rational cohomology torus constructed by Debarre--Jiang--Lahoz. Consequently, we disprove Kotschick's conjecture, the remaining implication in the Bobadilla--Kollár conjecture, and a conjecture of the first-named author.
CommentsThe paper is superseded by arXiv:2608.10973
