Rational manifolds and Calabi-Yau manifolds in the view of complex dymanics

2014 Fiscal Year Final Research Report

• Project/Area Number: 22340009
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Algebra
• Research Institution: Osaka University
• Principal Investigator: OGUISO Keiji 大阪大学, 理学(系)研究科(研究院), 教授 (40224133)
• Co-Investigator(Kenkyū-buntansha): KONNO Kazuhiro 大阪大学, 大学院理学研究科, 教授 (10186869) ; GOTO Ryuushi 大阪大学, 大学院理学研究科, 教授 (30252571) ; TAKAHASHI Atsushi 大阪大学, 大学院理学研究科, 教授 (50314290) ; SUMI Hiroki 大阪大学, 大学院理学研究科, 准教授 (40313324) ; FUJIKI Akira 大阪大学, その他部局等, 名誉教授 (80027383) ; USUI Sampei 大阪大学, その他部局等, 名誉教授 (90117002)
• Project Period (FY): 2010-04-01 – 2015-03-31
• Keywords: 双有理変換 / 双正則変換 / エントロピー / ダイナミカル次数 / 有理多様体 / カラビ・ヤウ多様体

Outline of Final Research Achievements

Blending birational algebraic geometry and complex dynamics, I found, in my own works and my joint works, the first explicit examples of three dimensional rational manifolds and Calabi-Yau manifolds with biregular primitive automorphisms of positive entropy, a complete affirmative answer to the Kawamata-Morrison cone conjecture when the manifolds are Calabi-Yau manifolds of Wheler type, of any dimension, an affirmative answer to the Ueno (Ueno-Camapana) problem on the unirationality of certain threefolds of quotient type, a negative answer to the Gizatullin problem on the automorphisms of quartic K3 surfaces and the Cremona group of the ambient projectitive three space, as well as some new applications of complex dynamics to the liftability problem of automorphisms of K3 surfaces in positive characteristic. These works are highly estimated and I was elected an invited speaker of the Internatioal Congress of Mathematicians 2014 held at Seoul, Korea.

Free Research Field

代数幾何学