Analysis reveals log canonical models of moduli spaces in pointed rational curves, suggesting connections to boundary coefficients and Deligne-Mostow quotients.
One of the ultimate goals of the Hassett-Keel program is the determination of the log canonical models of the moduli spaces of pointed rational curves M̄0,n. In this paper, we study log canonical models of M̄0,5 with asymmetric boundary divisors. Our results generalize previous work by Alexeev-Swinarski, Fedorchuk-Smyth, Kiem-Moon and Simpson for the case $n=5$. We prove that all moduli spaces of weighted pointed rational curves M̄0,A arise as log canonical models of M̄0,5 for suitable choices of boundary coefficients, thereby also recovering a theorem of Fedorchuk and Moon. In addition, we relate these moduli spaces to Deligne-Mostow ball quotients. We further study log canonical models of the moduli spaces M̄0,n· (1/k) with symmetric weight, which differ from M̄0,n.
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Hulek et al. (2025) studied this question.
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