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Classifies moduli spaces of 12 lines with a sextic point, indicating complex structure variability.
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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Amram et al. (2026) studied this question.
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