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March 21, 2026Open Access

Moduli Spaces of Arrangements of 12 Projective Lines with a Sextic Point

Key Points

The aim is to classify moduli spaces of arrangements of 12 projective lines featuring a sextic point.
Classified arrangements of 12 projective lines with a sextic point
Analyzed connected components in moduli spaces
Presented defining equations for non-irreducible moduli spaces
Evaluated the impact of complex conjugation on these arrangements
Identified multiple connected components in the moduli spaces
Provided defining equations for specific arrangements
Demonstrated potential for creating Zariski pairs after quotienting by complex conjugation

Abstract

In this paper, we classify moduli spaces of arrangements of 12 lines with a sextic point. We show that these moduli spaces can consist of more than two connected components. We also present defining equations of arrangements whose moduli spaces are not irreducible, and after taking quotients by complex conjugation, we obtain potential Zariski pairs.

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Cite This Study

Amram et al. (Fri,) studied this question.

synapsesocial.com/papers/69be35386e48c4981c673499 https://doi.org/https://doi.org/10.3390/math14061052

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