Cohomology formula for obstructions to asymptotic Chow semistability
TLDR
In this article, the intersection formula for the Donaldson-Futaki invariant was generalized to the case of higher FIFI invariants, which are obstructions to asymptotic Chow semistability.Abstract:
Odaka [16] and Wang [19] proved the intersection formula for the Donaldson-Futaki invariant. In this paper, we generalize this result for the higher Futaki invariants, which are obstructions to asymptotic Chow semistability.read more
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Deformation quantization and K\"ahler geometry with moment map
TL;DR: In this article, the authors formulate a cohomology formula for the invariant of K-stability condition on Kahler metrics with constant Cahen-Gutt momentum, and show that the constant scalar curvature Kahler metric problem and the study of deformation quantization meet at the notion of trace (density) for star product.
References
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Scalar Curvature and Stability of Toric Varieties
TL;DR: In this paper, a stability condition for a polarised algebraic variety is defined and a conjecture relating this to the existence of a Kahler metric of constant scalar curvature.
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Scalar Curvature and Projective Embeddings, I
TL;DR: In this article, it was shown that a metric of constant scalar curvature on a polarised Kahler manifold is the limit of metrics induced from a specific sequence of projective embeddings.
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Kahler-Einstein metrics on Fano manifolds, III: limits as cone angle approaches 2\pi\ and completion of the main proof
TL;DR: In this article, the Gromov-Hausdorff limits of metrics with cone singularities were studied in the case when the limiting cone angle approaches 2π, and it was shown that a K-stable Fano manifold admits a Kahler-Einstein metric.
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Extremal Kähler metrics and complex deformation theory
TL;DR: In this paper, the existence theorems for extremal Kahler metrics on certain compact complex surfaces were proved, and the authors applied these results to prove new existence theorem for compact manifolds of constant scalar curvature.
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A generalization of the Ross--Thomas slope theory
TL;DR: In this article, the authors give a formula for the Donaldson-Futaki invariants of certain type of semi test configurations, which essentially generalizes the Ross-Thomas slope theory.