The complex ball-quotient structure of the moduli space of certain sextic curves

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  • Zheng Zhiwei
    Yanqi Lake Beijing Institute of Mathematical Sciences and Applications
  • Zhong Yiming
    Beijing International Center for Mathematical Research, Peking University

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<p>We study moduli spaces of certain sextic curves with a singularity of multiplicity 3 from both perspectives of Deligne–Mostow theory and periods of 𝐾3 surfaces. In both ways we can describe the moduli spaces via arithmetic quotients of complex hyperbolic balls. We show in Theorem 7.4 that the two ball-quotient constructions can be unified in a geometric way.</p>

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