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Last modified date：2023.12.10

Assistant Professor / Division of Fundamental mathematics
Institute of Mathematics for Industry




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https://kyushu-u.elsevierpure.com/en/persons/noriyuki-hamada
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1. Noriyuki Hamada, Kenta Hayano, Topology of holomorphic Lefschetz pencils on the four-torus, Algebraic and Geometric Topology, 10.2140/agt.2018.18.1515, 18, 3, 1515-1572, 2018.04, © 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..
2. Noriyuki HAMADA, Kenta HAYANO, Classification of genus-1 holomorphic Lefschetz pencils, TURKISH JOURNAL OF MATHEMATICS, 10.3906/mat-2008-88, 45, 3, 1079-1119, 2021.05.
3. R. İnanç Baykur, Noriyuki Hamada, Lefschetz fibrations with arbitrary signature, Journal of the European Mathematical Society, 10.4171/jems/1326, 2023.03.
Membership in Academic Society
  • The Mathematical Society of Japan


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