Zariski multiples associated with quartic curves

Ichiro Shimada

Journal of Singularities
volume 24 (2022), 169-189

Received: 21 November 2021. Received in revised form: 24 September 2022.

DOI: 10.5427/jsing.2022.24g

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Abstract:

We investigate reducible plane curves whose irreducible components are a general smooth quartic curve, some of its bitangents, and some of its 4-tangent conics. We show that the deformation types of plane curves of this type coincide with the homeomorphism types. The number of deformation types grows as the 62nd power of the degree of the plane curves when the degree tends to infinity. Thus we obtain Zariski multiples of large sizes.

2020 Mathematical Subject Classification:

14H50, 14J26

Author(s) information:

Ichiro Shimada
Department of Mathematics
Graduate School of Science
Hiroshima University
1-3-1 Kagamiyama
Higashi-Hiroshima, 739-8526 JAPAN
email: ichiro-shimada@hiroshima-u.ac.jp