A lower bound on the Calabi functional for degenerations of polarized varieties is proven in terms of CM degree differences, viewed as a discretely valued version of Donaldson's bound.
On the Yau-Tian-Donaldson conjecture for weighted cscK metrics
5 Pith papers cite this work. Polarity classification is still indexing.
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K-polystable smooth Fano threefolds with ample Q-divisor polarization have reductive automorphism groups.
Gromov-Hausdorff convergence of non-collapsed polarized cscK surfaces is realized as Hilbert scheme convergence, with Bergman kernel estimates enabling Zariski openness of cscK metrics in smooth polarized families.
A survey tracing the development of weighted extremal Kähler metrics and reviewing recent work on the YTD conjecture for their existence.
A survey of key results and open problems in the metric geometry of the space of Kähler metrics over the last ten years.
citing papers explorer
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A lower bound on the Calabi functional for a degeneration of polarized varieties
A lower bound on the Calabi functional for degenerations of polarized varieties is proven in terms of CM degree differences, viewed as a discretely valued version of Donaldson's bound.
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A Matsushima theorem for K-polystable polarised smooth Fano threefolds
K-polystable smooth Fano threefolds with ample Q-divisor polarization have reductive automorphism groups.
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On the geometry of non-collapsed polarized cscK surfaces
Gromov-Hausdorff convergence of non-collapsed polarized cscK surfaces is realized as Hilbert scheme convergence, with Bergman kernel estimates enabling Zariski openness of cscK metrics in smooth polarized families.
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On weighted extremal K\"ahler metrics
A survey tracing the development of weighted extremal Kähler metrics and reviewing recent work on the YTD conjecture for their existence.
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A decade of metric geometry in the space of K\"ahler metrics
A survey of key results and open problems in the metric geometry of the space of Kähler metrics over the last ten years.