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<p>In this paper, we continue the study of the embedded topology of plane algebraic curves. We study the realization space of conic-line arrangements of degree 7 with certain fixed combinatorics and determine the number of connected components. This is done by showing the existence of a Zariski pair having these combinatorics, which we identified as a <i>π</i><sub>1</sub>-equivalent Zariski pair whose fundamental groups are free abelian with three generators.</p>

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The realization space of a certain conic-line arrangement of degree 7 and a π1-equivalent Zariski pair

  • 期刊论文

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  • 发表日期：

    2025年11月30日

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  • Meirav Amram,
  • Shinzo Bannai,
  • Taketo Shirane,
  • Uriel Sinichkin,
  • Hiro-o Tokunaga

摘要

In this paper, we continue the study of the embedded topology of plane algebraic curves. We study the realization space of conic-line arrangements of degree 7 with certain fixed combinatorics and determine the number of connected components. This is done by showing the existence of a Zariski pair having these combinatorics, which we identified as a π1-equivalent Zariski pair whose fundamental groups are free abelian with three generators.