Degenerations of Fano and Calabi-Yau varieties and its applications

• Project/Area Number: 23K03032
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 11010:Algebra-related
• Research Institution: Kobe University
• Principal Investigator: 佐野 太郎 神戸大学, 理学研究科, 准教授 (10773195)
• Project Period (FY): 2023-04-01 – 2028-03-31
• Project Status: Granted (Fiscal Year 2023)
• Budget Amount: ¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000); Fiscal Year 2027: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2026: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2025: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2024: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2023: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
• Keywords: Fano多様体 / Calabi-Yau多様体 / 退化

Outline of Research at the Start

本研究では代数多様体, 主にFano多様体およびCalabi-Yau多様体の退化の性質を調べ, それら代数多様体の分類の進展を目指す。具体的には, 退化の条件をつけた下でのCalabi-Yau多様体の族の有界性、および具体的なFano多様体のK-安定性, 変形の障害などを調べる。対数的Calabi-Yau多様体の対数変形理論を発展させ, その応用として興味深いCalabi-Yau多様体の例を構成することも目指す。