AI 中文总结
本文证明所有维数下K-平凡簇的有限性结果，利用极化K3曲面的整体托雷利定理建立纤维同构的霍奇理论充分条件，并应用于双有理等价纤维稠密的射影族，得出所有纤维同构的结论。
AI 中文摘要
本文证明了所有维数下K-平凡簇的有限性结果。在二维情形下，这些结果是极化K3曲面的整体托雷利定理的推论。特别地，我们建立了一个充分条件，即当K-平凡簇的射影族的两个纤维通过霍奇理论同构时，该条件成立。作为应用，我们证明若K-平凡簇的射影族包含一个由双有理等价纤维构成的稠密子集，则所有纤维均同构。
英文摘要
In this paper, we prove finiteness results for K-trivial varieties in all dimensions. In dimension 2, these results are corollaries of the Global Torelli Theorem for polarized K3 surfaces. In particular, we establish a sufficient condition when two fibers of a projective family of K-trivial varieties are isomorphic via the Hodge theory. As applications, we prove that if a projective family of K-trivial varieties has a dense subset of birationally equivalent fibers, then all fibers are isomorphic.
Commentscomments very welcome!
