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

Meirav Amram; Eran Lieberman; Sheng Li Tan; Mina Teicher; Xiao Hang Wu

doi:10.3390/math14061052

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

Meirav Amram
, Eran Lieberman
, Sheng Li Tan
, Mina Teicher
, Xiao Hang Wu^*

^*Corresponding author for this work

School of Mathematical Sciences

Sami Shamoon College of Engineering
Bar-Ilan University
Wuhan University of Science and Technology

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Article number	1052
Journal	Mathematics
Volume	14
Issue number	6
DOIs	https://doi.org/10.3390/math14061052
State	Published - Mar 2026

Keywords

classification of algebraic curves
line arrangements
moduli spaces
Zariski pairs

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10.3390/math14061052

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title = "Moduli Spaces of Arrangements of 12 Projective Lines with a Sextic Point",

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.",

keywords = "classification of algebraic curves, line arrangements, moduli spaces, Zariski pairs",

author = "Meirav Amram and Eran Lieberman and Tan, \{Sheng Li\} and Mina Teicher and Wu, \{Xiao Hang\}",

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AU - Amram, Meirav

AU - Lieberman, Eran

AU - Tan, Sheng Li

AU - Teicher, Mina

AU - Wu, Xiao Hang

PY - 2026/3

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N2 - 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.

AB - 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.

KW - classification of algebraic curves

KW - line arrangements

KW - moduli spaces

KW - Zariski pairs

UR - https://www.scopus.com/pages/publications/105034450783

U2 - 10.3390/math14061052

DO - 10.3390/math14061052

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JO - Mathematics

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

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Keywords

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