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

Key Points

Connected components highlight the structure of realizations in conic-line arrangements, enhancing our understanding of embedded topology.
Three generators characterize the free abelian fundamental groups related to the identified Zariski pair, illustrating unique algebraic properties.
Observational analysis of degree 7 conic-line arrangements elucidates complex combinatorics in algebraic geometry, particularly plane curves.
Findings suggest implications for deeper study of Zariski pairs, potentially leading to novel insights in algebraic topology.

Abstract

Abstract 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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