| Budget Amount *help |
¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| 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.
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