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.
CM Stability and the Generalized Futaki Invariant I
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abstract
Based on the Cayley, Grothendieck, Knudsen Mumford theory of determinants we extend the CM polarization to the Hilbert scheme. We identify the weight of this refined line bundle with the generalized Futaki invariant of Donaldson. We are able to conclude that CM stability implies K-Stability. An application of the Grothendieck Riemann Roch Theorem shows that this refined sheaf is isomorphic to the CM polarization introduced by Tian in 1994 on any closed, simply connected base .
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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.