发表机构
Westlake University; Southern University of Science and Technology（西湖大学; 南方科技大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究固定光滑射影簇，探讨klt边界变化时其对数典范模型的有限性，证明一般型或不规则光滑射影曲面的对数典范模型有限，构造出具无穷多此类模型的曲面与三维簇，补充了相关猜想与定理的边界情况。
AI 中文摘要
受将Morrison-Kawamata锥猜想推广到Calabi-Yau簇之外，以及不一定是一般型的满射目标有限性的Severi-Maehara型结果的启发，我们固定一个光滑射影簇，研究当klt边界变化时其对数典范模型的有限性。这两种推广在一般情况下均不成立。我们证明，对于一般型或不规则的光滑射影曲面，其对数典范模型具有有限性；反之，对于每个κ∈{-∞,0,1}，我们构造了一个Kodaira维数为κ的光滑射影非极小曲面，它具有无穷多个对数典范模型，而一大类极小曲面的对数典范模型具有有限性。在高维情形下，我们构造了一个具有丰富典范除子的光滑三维簇，它具有无穷多个对数典范模型，这与Tsai的定理形成对比，Tsai的定理指出这类模型中仅有有限多个可以是光滑的。
英文摘要
Motivated by extending the Morrison-Kawamata cone conjecture beyond Calabi-Yau varieties and Severi-Maehara type finiteness results to targets not necessarily of general type, we fix a smooth projective variety and study the finiteness of its log canonical models as klt boundaries vary. Our main result establishes finiteness for every smooth projective minimal surface. For each $κ\in\{-\infty,0,1\}$, we construct a smooth projective non-minimal surface of Kodaira dimension $κ$ with infinitely many log canonical models, showing that the minimality assumption cannot be omitted in general. We also investigate possible extensions of this finiteness result to higher dimensions.
Comments30 pages; a conjecture from the version 1 is solved with the assistance of ChatGPT
