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arXiv · 2209.11938

Zariski multiples associated with quartic curves

Ichiro Shimada
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Abstract

We investigate Zariski multiples of plane curves $Z_1, \dots, Z_N$ such that each $Z_i$ is a union of a smooth quartic curve, some of its bitangents, and some of its 4-tangent conics. We show that, for plane curves of this type, the deformation types are equal to the homeomorphism types, and that the number of deformation types grows as $O(d^{62})$ when the degree $d$ of the plane curves tends to infinity.

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Ichiro Shimada. 2022-09-24. Zariski multiples associated with quartic curves. https://arxiv.org/abs/2209.11938

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