Deformation and classification of Fano varieties and Calabi-Yau varieties

2019 Fiscal Year Final Research Report

• Project/Area Number: 16K17573
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Algebra
• Research Institution: Kobe University
• Principal Investigator: Sano Taro 神戸大学, 理学研究科, 助教 (10773195)
• Project Period (FY): 2016-04-01 – 2020-03-31
• Keywords: Fano多様体 / Calabi-Yau多様体 / 変形理論

Outline of Final Research Achievements

I studied several problems on Fano varieties and Calabi-Yau varieties which form building blocks in the classification theory. With Pizzato and Tasin, we solved the effective non-vanishing conjecture on weighted complete intersections. With Coughlan, we showed that many affine cones over K3 surfaces or Abelian varieties do not admit smoothings. With Okawa, we showed the non-commutative rigidity of the moduli stack of stable pointed curves except for finitely many cases. With Hashimoto, we constructed examples of non-Kahler Calabi-Yau 3-folds with arbitrarily large 2nd Betti numbers.

Free Research Field

代数幾何学

Academic Significance and Societal Importance of the Research Achievements

代数多様体の分類理論は代数幾何学における中心的な話題であり、その核となるFano多様体、Calabi-Yau多様体の分類を進めるのは意義がある。また、最近はFano多様体に関連する研究の進展は目覚ましく、注目度は高い。Calabi-Yau多様体に関連する研究はFano多様体に比べると小康状態であるが、次に目覚ましい進展が訪れる可能性があり、アイデアを積み重ねる価値がある分野と思う。