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Trisections on certain rational elliptic surfaces and families of Zariski pairs degenerating to the same conic-line arrangement

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Abstract

In this paper, we study the geometry of trisections of certain rational elliptic surfaces. We utilize Mumford representations of semi-reduced divisors in our study and demonstrate its effectiveness in dealing with equations of trisections and related plane curves. As an application, we construct plane curves with interesting properties. Especially, we give explicit equations of plane curves which give a family of Zariski pairs consisting of cubic-conic-line arrangements that degenerate to the same conic-line arrangement.

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Funding

The first author is partially supported by Grant-in-Aid for Scientific Research C (18K03263). The last author is partially supported by Grant-in-Aid for Scientific Research C (20K03561).

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Authors and Affiliations

  1. Department of Applied Mathematics, Faculty of Science, Okayama University of Science, 1-1 Ridai-cho, Kita-ku, Okayama-shi, Okayama, 700-0005, Japan

    S. Bannai

  2. Department of Mathematical Sciences, Graduate School of Science, Tokyo Metropolitan University, 1-1 Minami-Ohsawa, Hachiohji, 192-0397, Japan

    N. Kawana, R. Masuya & H. Tokunaga

Authors
  1. S. Bannai
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  2. N. Kawana
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  3. R. Masuya
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  4. H. Tokunaga
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Contributions

H.Tokunaga and S. Bannai contributed by conceiving the main conceptual ideas and giving the outline of the proof. R. Masuya contributed to some details of the proof and computations of the examples. N. Kawana contributed to the computations of the examples.

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Correspondence to S. Bannai.

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Bannai, S., Kawana, N., Masuya, R. et al. Trisections on certain rational elliptic surfaces and families of Zariski pairs degenerating to the same conic-line arrangement. Geom Dedicata 216, 8 (2022). https://doi.org/10.1007/s10711-021-00672-5

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  • DOI: https://doi.org/10.1007/s10711-021-00672-5

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