Nodal curves with a contact-conic and Zariski pairs-Reference-Cited by-同舟云学术

Nodal curves with a contact-conic and Zariski pairs

Published:2019-09-11 Issue:4 Volume:19 Page:555-572
ISSN:1615-7168
Container-title:Advances in Geometry
language:en
Short-container-title:

Author:

Bannai Shinzo¹,Shirane Taketo²

Affiliation:

1. Department of Natural Sciences , National Institute of Technology , Ibaraki College, 866 Nakane , Hitachinaka , Ibaraki 312-8508 , Japan

2. Department of Mathematics, Faculty of Science and Technology , Tokushima University , 2-1 Minamijosanjima-cho , Tokushima , 770-8506 , Japan

Abstract

Abstract To study the splitting of nodal plane curves with respect to contact conics, we define the splitting type of such curves and show that it can be used as an invariant to distinguish the embedded topology of plane curves. We also give a criterion to determine the splitting type in terms of the configuration of the nodes and tangent points. As an application, we construct sextics and contact conics with prescribed splitting types, which give rise to new Zariski-triples.

Publisher

Walter de Gruyter GmbH

Subject

Geometry and Topology

Link

https://www.degruyter.com/document/doi/10.1515/advgeom-2018-0032/pdf

Reference19 articles.

1. E. Artal-Bartolo, Sur les couples de Zariski. J. Algebraic Geom. 3 (1994), 223–247. MR1257321 Zbl 0823.14013

2. E. Artal Bartolo, J. Carmona Ruber, J. I. Cogolludo Agustín, Braid monodromy and topology of plane curves. Duke Math. J. 118 (2003), 261–278. MR1980995 Zbl 1058.14053

3. E. Artal Bartolo, J. I. Cogolludo, H. Tokunaga, A survey on Zariski pairs. In: Algebraic geometry in East Asia—Hanoi 2005, volume 50 of Adv. Stud. Pure Math., 1–100, Math. Soc. Japan, Tokyo 2008. MR2409555 Zbl 1141.14015

4. E. Artal Bartolo, H. Tokunaga, Zariski k-plets of rational curve arrangements and dihedral covers. Topology Appl. 142 (2004), 227–233. MR2071304 Zbl 1075.14013

5. S. Bannai, A note on splitting curves of plane quartics and multi-sections of rational elliptic surfaces. Topology Appl. 202 (2016), 428–439. MR3464177 Zbl 1342.14080

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