All moduli spaces of weighted pointed rational curves for five points arise as log canonical models of the unweighted space with suitable asymmetric boundary coefficients, generalizing prior results and relating to Deligne-Mostow quotients.
K-moduli of Fano threefolds and genus four curves
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K-moduli spaces of specific weighted hypersurfaces are described explicitly via wall-crossing on log Fano pairs, coinciding with GIT variation except for a divisorial contraction at the final wall, yielding new birational models for loci in marked hyperelliptic curve moduli.
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Remarks on two problems by Hassett
All moduli spaces of weighted pointed rational curves for five points arise as log canonical models of the unweighted space with suitable asymmetric boundary coefficients, generalizing prior results and relating to Deligne-Mostow quotients.