Updated on 2024/06/19

Affiliated organization, Waseda University Senior High School
Job title
Teacher (Affiliated Senior High School)
Doctor of science ( 2022.03 Waseda University )

Research Areas

  • Algebra   代数幾何学


  • SNC Log Symplectic Structures on Fano Products

    Katsuhiko Okumura

    Canadian Mathematical Bulletin   63 ( 4 ) 891 - 900  2020.12

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    <title>Abstract</title>This paper classifies Poisson structures with the reduced simple normal crossing divisor on a product of Fano varieties of Picard number 1. The characterization of even-dimensional projective spaces from the viewpoint of Poisson structures is given by Lima and Pereira. In this paper, we generalize the characterization of projective spaces to any dimension.


  • A classification of SNC log symplectic structures on blow-up of projective spaces

    Katsuhiko Okumura

    Letters in Mathematical Physics   110 ( 10 ) 2763 - 2778  2020.10



Research Projects

  • Construtions of log symplectic structures which characterize quadric hypersurfaces and projective spaces.

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Research Activity Start-up

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Internal Special Research Projects

  • V-NC対数的シンプレクティック構造の分類とトーリックファノ多様体


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  • 点のヒルベルトスキームを用いたSNCログシンプレクティック構造の構成


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  • Fano多様体を特徴づける対数的シンプレクティック構造の構成


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    The original plan was to study Poisson structures that characterize quadratic hypersurfaces. However, my interest shifted to the construction of SNC log-symplectic structures using the Hilbert scheme of points, which I was studying in parallel, and I spent most of this year working on this topic. It is a kind of Poisson structure known as the closest one to symplectic and it characterize projectice space. It is also difficult to construct examples like the symplectic case. We find that the blow-up of the Hilbert scheme of points of the diagonal Poisson structure on the projective space form an example of SNC log-symplectic. We also started a study on a VNC log-symplectic structure, which is a generalization of SNC that allows actions of finite groups.