K-stability, degeneration of algebraic varieties

2016 Fiscal Year Final Research Report

• Project/Area Number: 26870316
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Geometry; Algebra
• Research Institution: Kyoto University
• Principal Investigator: Odaka Yuji 京都大学, 理学研究科, 准教授 (30700356)
• Project Period (FY): 2014-04-01 – 2017-03-31
• Keywords: モジュライ空間 / 安定性 / 標準Kahler計量

Outline of Final Research Achievements

I improved the understanding of stability and moduli of algebraic varieties or arithmetic varieties. I constructed compact algebraic space of KE Fano smoothable varieties. I generalized so-called Faltings height to general arithmetic varieties as modular heights, and then established the basic of arithmetic or Arakelov theoretic aspect of the K-stability and canonical Kahler metrics. I also introduced what I call tropical geometric compactifications of moduli spaces and studied the structure in details. It is closely related to geometric aspect of Mirror symmetry (after Strominger-Yau-Zaslow), tropical geometry and non-archimedean geometry.

Free Research Field

代数幾何学とその関連分野