Analysis reveals a Zariski pair with free abelian fundamental groups, indicating connected components in conic-line arrangements.
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 π 1 -equivalent Zariski pair whose fundamental groups are free abelian with three generators.
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Amram et al. (2025) studied this question.
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