カラビ・ヤウ多様体の錐予想について

关于Calabi-Yau流形的锥猜想

• 批准号: 21J10242
• 负责人: WANG Long
• 金额: $ 0.96万
• 依托单位: The University of Tokyo
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for JSPS Fellows
• 财政年份: 2021
• 资助国家: 日本
• 起止时间: 2021-04-28 至 2023-03-31
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-21J10242/
• 关键词: Calabi-Yau variety; Cone conjecture; Dynamical degree; Arithmetic degree; Calabi－Yau varieties; Birational automorphisms; Arithmetic degrees; Dynamical degrees

Calabi-Yau varieties play a prominent role in many branches of mathematics including algebraic geometry. The mirror symmetry of Calabi-Yau varieties enlightened D. Morrison to formulate the cone conjecture. Y. Kawamata proposed a refinement whose motivation originated from birational geometry. In this direction, besides two published papers, I completed one preprint.The study of the birational automorphism groups is not only interrelated with the cone conjecture but also of independent interest. One attractive area is the dynamics of birational automorphisms from both geometric and arithmetic viewpoints. Recently, S. Kawaguchi and J. H. Silverman proposed a conjecture which connects dynamical and arithmetic degrees of dominant rational self-maps. This conjecture is known for some cases of morphisms, but is much less known for arbitrary rational maps due to the lack of functoriality of height functions. In this direction, besides two published papers, I completed two preprints.

Calabi-yau品种在包括代数几何形状在内的许多数学分支中起着重要的作用。卡拉比（Calabi-Yau）品种的镜子对称性启发了莫里森（D. Y. Kawamata提出了一种改进，其动机起源于Birational几何形状。在这个方向上，除了两篇已发表的论文外，我还完成了一个预印本。对男子式自动形态群体的研究不仅与圆锥体构想相互关联，而且具有独立的兴趣。一个有吸引力的领域是从几何和算术观点均来自生育自动形态的动力学。最近，S。Kawaguchi和J. H. Silverman提出了一个猜想，该猜想连接了主导理性自图的动力学和算术程度。该猜想是某些形态的众所周知的，但由于缺乏高度功能的功能性，由于任意有理图而闻名。在这个方向上，除了两篇已发表的论文外，我还完成了两个预印本。

项目成果

Remarks on nef and movable cones of hypersurfaces in Mori dream spaces

森梦空间中的nef和超曲面可动锥评述

• DOI: 10.1016/j.jpaa.2022.107101
• 发表时间: 2022
• 期刊: Journal of Pure and Applied Algebra
• 影响因子: 0.8
• 作者: 安部清尚;他 KamLAND コラボレーション;Zhou Yiwen;Wang Long
• 通讯作者: Wang Long

On automorphisms of Hilbert squares of smooth hypersurfaces

光滑超曲面希尔伯特平方的自同构

• DOI: 10.1080/00927872.2022.2107209
• 发表时间: 2022
• 期刊: Communications in Algebra
• 影响因子: 0.7
• 作者: Oki Yuichiro;Harano Kodai;Hara Yuichi;Sasajima Yoshiyuki;Sasaki Ryo;Ito Takanori;Fujishiro Mitsuhiro;Ito Taichi;Wang Long
• 通讯作者: Wang Long

Arithmetic degrees and Zariski dense orbits of dominant rational self-maps

占主导地位的理性自映射的算术度和 Zariski 稠密轨道

• 发表时间: 2022
• 作者: Adiza Abass;Tokuju Okano;Kotchakorn Boonyaleka;RyoKinoshita-Daitoku;Shoji Yamaoka;Hiroshi Ashida;Toshihiko Suzuki;土橋祥平・吉原利典・安藤大輔・内藤久士・小山勝弘;土橋祥平・吉原利典・内藤久士;Wang Long;Wang Long;Wang Long;Wang Long
• 通讯作者: Wang Long

On automorphisms and the cone conjecture for Enriques surfaces in odd characteristic

奇特性Enriques曲面的自同构与锥猜想

• DOI: 10.4310/mrl.2021.v28.n4.a14
• 发表时间: 2021
• 期刊: Mathematical Research Letters
• 影响因子: 1
• 作者: Yuuki Hayashi;Yukinari Sumino;Hiromasa Takaura;Wang Long
• 通讯作者: Wang Long