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Advances in Geometry

Managing Editor: Grundhöfer, Theo / Joswig, Michael

Editorial Board: Bamberg, John / Bannai, Eiichi / Cavalieri, Renzo / Coskun, Izzet / Duzaar, Frank / Eberlein, Patrick / Gentili, Graziano / Henk, Martin / Kantor, William M. / Korchmaros, Gabor / Kreuzer, Alexander / Lagarias, Jeffrey C. / Leistner, Thomas / Löwen, Rainer / Ono, Kaoru / Ratcliffe, John G. / Scheiderer, Claus / Van Maldeghem, Hendrik / Weintraub, Steven H. / Weiss, Richard

IMPACT FACTOR 2018: 0.789

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Volume 19, Issue 4


Nodal curves with a contact-conic and Zariski pairs

Shinzo Bannai
  • Department of Natural Sciences, National Institute of Technology, Ibaraki College, 866 Nakane, Hitachinaka, Ibaraki 312-8508, Japan
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/ Taketo Shirane
  • Corresponding author
  • Department of Mathematics, Faculty of Science and Technology, Tokushima University, 2-1 Minamijosanjima-cho, Tokushima, 770-8506, Japan
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Published Online: 2019-09-11 | DOI: https://doi.org/10.1515/advgeom-2018-0032


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.

Keywords: Splitting curve; Zariski pair; double cover

MSC 2010: 14E20; 14H50; 32S50; 57N35


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About the article

(current address) and National Institute of Technology, Ube College, 2-14-1 Tokiwadai, Ube, Yamaguchi 755-8555, Japan

Received: 2017-05-31

Revised: 2017-10-27

Published Online: 2019-09-11

Published in Print: 2019-10-25

Communicated by: S. Weintraub

Citation Information: Advances in Geometry, Volume 19, Issue 4, Pages 555–572, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/advgeom-2018-0032.

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