Moduli spaces of algebraic varieties and self-morphisms

2017 Fiscal Year Final Research Report

• Project/Area Number: 25220701
• Research Category: Grant-in-Aid for Scientific Research (S)
• Allocation Type: Single-year Grants
• Research Field: Algebra
• Research Institution: Kyoto University
• Principal Investigator: Mukai Shigeru 京都大学, 数理解析研究所, 教授 (80115641)
• Co-Investigator(Kenkyū-buntansha): 中島 啓 京都大学, 数理解析研究所, 教授 (00201666) ; 吉川 謙一 京都大学, 理学研究科, 教授 (20242810) ; 小木曽 啓示 東京大学, 数理(科)学研究科(研究院), 助教授 (40224133) ; 森脇 淳 京都大学, 理学研究科, 教授 (70191062) ; 宍倉 光広 京都大学, 理学研究科, 教授 (70192606)
• Co-Investigator(Renkei-kenkyūsha): UEDA Tetsuo 京都大学, 理学研究科, 名誉教授 (10127053) ; NAKAYAMA Noboru 京都大学, 数理解析研究所, 准教授 (10189079) ; NAMIKAWA Yoshinori 京都大学, 理学研究科, 教授 (80228080) ; KAWAGUCHI Shu 同志社大学, 理工学部, 教授 (20324600) ; ABE Takeshi 熊本大学, 自然科学研究科, 准教授 (90362409) ; NASU Hirokazu 東海大学, 理学部, 講師 (30535331) ; OHASHI Hisanori 東京理科大学, 理工学部, 講師 (40547006) ; MA Shohei 東京工業大学, 理工学研究科, 准教授 (80633255)
• Research Collaborator: WANDEL Marte , 特定研究員 ; KIM Kyounghee Florida State University, 准教授 ; DOLGACHEV Igor University of Michigan, 名誉教授 ; ALLCOCK Daniel University of Texas at Austin, 教授 ; HEDEN Isac , 外国人特別研究者 ; SANNAI Akiyoshi , 特定助教
• Project Period (FY): 2013-05-31 – 2018-03-31
• Keywords: 代数幾何学 / 複素幾何 / 複素力学系 / 表現論 / アラケロフ幾何 / 幾何学的群論

Outline of Final Research Achievements

Adding to the key concept “self-morphism” to the study of algebraic varieties, we obtained many of findings in these five years. Among them we introduced the virtual cohomological dimension in the study of infinite discrete automorphism groups of Enriques surfaces. Hopefully this will stimulate two fields, algebraic geometry and discrete groups. Since Enriques surfaces mildly degenerate to rational surfaces, this has an application to the Cremona group of two variables. The study of nine mirror families of Enriques surfaces was developed by Mukai and Ohashi more than expected. Oguiso and his collaborators constructed primitive 3-fold automorphisms of positive entropy and a remarkable projective algebraic surface whose automorphism group is discrete but not finitely generated. The study of analytic torsion of K3 surfaces with involution was also much developed by Yoshikawa and Ma.

Free Research Field

代数幾何学