AI 中文总结
该研究证明了两类纤维化不存在余维一多重纤维的结论，为拉格朗日纤维化结构、相关猜想及卡拉比-丘纤维化研究提供了关键进展，仅存在一个奇维K-平凡簇的例外情形。
AI 中文摘要
我们证明，在射影空间上具有拉格朗日纤维化的紧致超凯勒流形不存在余维一的多重纤维。这对拉格朗日纤维化的结构有若干推论，包括在关于一般奇异纤维的Sawon猜想上取得进展、Kamenova-Lu反双曲性，以及将内龙（Néron）模型作用扩展到基的一个大开子集。我们对单连通K-平凡簇上的卡拉比-丘纤维化（包括椭圆纤维化）也证明了相同结果，仅存在一个例外：奇维K-平凡簇在射影线上具有一个重数为2的纤维，该例外情形由Borisov-Nuer的例子及其推广实现。
英文摘要
We prove that compact hyper-Kähler manifolds with a Lagrangian fibration over a projective space have no multiple fibers in codimension one. This has several consequences for the structure of Lagrangian fibrations, including progress on Sawon's conjecture on general singular fibers, Kamenova--Lu anti-hyperbolicity, and the extension of the Néron model action to a big open subset of the base. We prove the same result for Calabi--Yau fibrations on simply-connected K-trivial varieties, including elliptic fibrations, with a single exceptional case: an odd-dimensional K-trivial variety with a single fiber of multiplicity 2 over the projective line. This exceptional case is realized by examples of Borisov--Nuer and their generalizations.
