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Algebra i Analiz, 2022, Volume 34, Issue 5, Pages 1–22 (Mi aa1829)  
This article is cited in 1 scientific paper (total in 1 paper)

Research Papers

Torsion divisors of plane curves and Zariski pairs

E. Artal Bartoloa, Sh. Bannaib, T. Shiranec, H. Tokunagad

a Departamento de Matemaáticas, IUMA, Universidad de Zaragoza, C. Pedro Cerbuna 12, 50009 Zaragoza, Spain
b Department of Applied Mathematics, Faculty of Science, Okayama University of Science, 1-1 Ridai-cho Kita-ku Okayama-shi, Okayama 700-0005, Japan
c Department of Mathematical Sciences, Faculty of Science and Technology, Tokushima University, Tokushima, 770-8502, Japan
d Department of Mathematical Sciences, Graduate School of Science, Tokyo Metropolitan University, 1-1 Minami-Ohsawa, Hachiohji, 192-0397, Japan
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Abstract: This paper is devoted to the study of the embedded topology of reducible plane curves having a smooth irreducible component. In previous studies, the relationship between the topology and certain torsion classes in the Picard group of degree zero of the smooth component was implicitly considered. Here this relationship is formulated clearly and a criterion is given for distinguishing the embedded topology in terms of torsion classes. Furthermore, a method is presented for systematically constructing examples of curves where this criterion is applicable, and new examples of Zariski $N$-tuples are produced.
Keywords: Plane curve arrangements, torsion divisors, splitting numbers, Zariski pairs.
Funding agency Grant number
Japan Society for the Promotion of Science 18K03263
21K03182
17K05205
Ministerio de Ciencia, Innovacin y Universidades Agencia Estatal de Investigacin PID2020-114750GB-C31/AEI/10.13039/501100011033
E. A. B.: Partially supported by PID2020-114750GB-C31/AEI/10.13039/501100011033 and Departamento de Ciencia, Universidad y Sociedad del Conocimiento of the Gobierno de Aragón (E22_20R: “Álgebra y Geometría”).
Sh. B.: Partially supported by Grant-in-Aid for Scientific Research C (18K03263).
T. Sh.: Partially supported by Grant-in-Aid for Scientific Research C (21K03182), corresponding author.
H. T.: Partially supported by Grant-in-Aid for Scientific Research C (17K05205).
Received: 22.09.2021
English version:
St. Petersburg Mathematical Journal, 2023, Volume 34, Issue 5, Pages 721–736
DOI: https://doi.org/10.1090/spmj/1776
Document Type: Article
Language: English
Citation: E. Artal Bartolo, Sh. Bannai, T. Shirane, H. Tokunaga, “Torsion divisors of plane curves and Zariski pairs”, Algebra i Analiz, 34:5 (2022), 1–22; St. Petersburg Math. J., 34:5 (2023), 721–736
Citation in format AMSBIB
\Bibitem{ArtBanShi22}
\by E.~Artal Bartolo, Sh.~Bannai, T.~Shirane, H.~Tokunaga
\paper Torsion divisors of plane curves and Zariski pairs
\jour Algebra i Analiz
\yr 2022
\vol 34
\issue 5
\pages 1--22
\mathnet{http://mi.mathnet.ru/aa1829}
\transl
\jour St. Petersburg Math. J.
\yr 2023
\vol 34
\issue 5
\pages 721--736
\crossref{https://doi.org/10.1090/spmj/1776}
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    • This publication is cited in the following 1 articles:
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    		Алгебра и анализ St. Petersburg Mathematical Journal
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