The Picard number of Fano manifolds

2016 Fiscal Year Final Research Report

• Project/Area Number: 15H06690
• Research Category: Grant-in-Aid for Research Activity Start-up
• Allocation Type: Single-year Grants
• Research Field: Algebra
• Research Institution: Waseda University
• Principal Investigator: SUZUKI Taku 早稲田大学, 理工学術院, 助教 (60754885)
• Project Period (FY): 2015-08-28 – 2017-03-31
• Keywords: ファノ多様体 / 有理曲線 / ピカール数 / 射影空間 / 収縮射 / 極小有理曲線族 / スロープ安定性

Outline of Final Research Achievements

For the research task "The Picard number of Fano manifolds", I investigated (1) the Picard number of Fano manifolds in terms of their extremal contractions, (2) higher order minimal families of rational curves associated to Fano manifolds, and (3) slope stability of Fano manifolds. In (1), I proved that Mukai conjecture holds for Fano 6-folds admitting no small contractions. In (2), I introduced higher order minimal families of rational curves associated to Fano manifolds X and a new invariant N(X) as the maximal order of them, and I provided a sufficient condition for Fano manifolds X to have large N(X). In (3), I classified special Fano manifolds with Picard number at most two which are not slope stable

Free Research Field

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