The realization space of a certain conic line arrangement of degree 7 and a $\pi_1$-equivalent Zariski pair

Author:

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

Keyword:

Mathematics, Algebraic Geometry, Algebraic Geometry (math.AG), Combinatorics (math.CO), Geometric Topology (math.GT)

journal:

date:

2023-07-03 16:00:00

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 $\pi_1$-equivalent Zariski pair.

PDF: The realization space of a certain conic line arrangement of degree 7 and a $\pi_1$-equivalent Zariski pair.pdf