Explicit optimal degenerations are found for Fano threefolds in family 2.23 yielding weighted K-polystable KRS limits, with moduli spaces isomorphic to GIT of biconic curves or a single point according to the H-invariant.
On positivity of the CM line bundle on K -moduli spaces
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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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Optimal Degenerations of K-unstable Fano threefolds
Explicit optimal degenerations are found for Fano threefolds in family 2.23 yielding weighted K-polystable KRS limits, with moduli spaces isomorphic to GIT of biconic curves or a single point according to the H-invariant.
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Wall-crossing for K-moduli spaces of certain families of weighted projective hypersurfaces
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.