Hayano, Kenta

写真a

Affiliation

Faculty of Science and Technology, Department of Mathematics (Yagami)

Position

Associate Professor

Related Websites

 

Papers 【 Display / hide

  • Topology of holomorphic lefschetz pencils on the four-torus

    Hamada N., Hayano K.

    Algebraic and Geometric Topology (Algebraic and Geometric Topology)  18 ( 3 ) 1515 - 1572 2018.04

    ISSN  14722747

     View Summary

    © 2018, Mathematical Sciences Publishers. All rights reserved. We discuss topological properties of holomorphic Lefschetz pencils on the four-torus. Relying on the theory of moduli spaces of polarized abelian surfaces, we first prove that, under some mild assumptions, the (smooth) isomorphism class of a holomorphic Lefschetz pencil on the four-torus is uniquely determined by its genus and divisibility. We then explicitly give a system of vanishing cycles of the genus-3 holomorphic Lefschetz pencil on the four-torus due to Smith, and obtain those of holomorphic pencils with higher genera by taking finite unbranched coverings. One can also obtain the monodromy factorization associated with Smith’s pencil in a combinatorial way. This construction allows us to generalize Smith’s pencil to higher genera, which is a good source of pencils on the (topological) four-torus. As another application of the combinatorial construction, for any torus bundle over the torus with a section we construct a genus-3 Lefschetz pencil whose total space is homeomorphic to that of the given bundle.

Papers, etc., Registered in KOARA 【 Display / hide

Presentations 【 Display / hide

Research Projects of Competitive Funds, etc. 【 Display / hide

  • 組み合わせ的手法による低次元シンプレクティック多様体の研究

    2017.04
    -
    2021.03

    MEXT,JSPS, Grant-in-Aid for Scientific Research, 早野 健太, Grant-in-Aid for Young Scientists (B), Principal Investigator

  • Topology of stable mappings and diagrams of four-manifolds

    2014.04
    -
    2018.03

    MEXT,JSPS, Grant-in-Aid for Scientific Research, 早野 健太, Grant-in-Aid for Young Scientists (B), Principal Investigator

 

Courses Taught 【 Display / hide

  • MATHEMATICS 1B

    2021

  • MATHEMATICS 1A

    2021

  • INDEPENDENT STUDY ON FUNDAMENTAL SCIENCE AND TECHNOLOGY

    2021

  • GRADUATE RESEARCH ON FUNDAMENTAL SCIENCE AND TECHNOLOGY 2

    2021

  • GRADUATE RESEARCH ON FUNDAMENTAL SCIENCE AND TECHNOLOGY 1

    2021

display all >>

 

Memberships in Academic Societies 【 Display / hide

  • 日本数学会, 

    2011.04
    -
    Present