On K-stability of reductive varieties
Valery Alexeev,Ludmil Katzarkov +1 more
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In this paper, a conjecture relating GIT stability of a polarized algebraic variety to the existence of a Kahler metric of constant scalar curvature was shown to hold for reductive algebraic varieties.Abstract:
G. Tian and S.K. Donaldson formulated a conjecture relating GIT stability of a polarized algebraic variety to the existence of a Kahler metric of constant scalar curvature. In [D3] Donaldson partially confirmed it in the case of projective toric varieties. In this paper we extend Donaldson’s results and computations to a new case, that of reductive varieties.read more
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Kahler geometry on toric manifolds, and some other manifolds with large symmetry
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Kähler–Einstein metrics along the smooth continuity method
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TL;DR: In this article, it was shown that if a Fano manifold is K-stable with respect to special degenerations equivariant under a compact group of automorphisms, then it admits a K\"ahler-Einstein metric.
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Kähler-Einstein metrics on group compactifications
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References
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Book
Introduction to Toric Varieties.
TL;DR: In this article, a mini-course is presented to develop the foundations of the study of toric varieties, with examples, and describe some of these relations and applications, concluding with Stanley's theorem characterizing the number of simplicies in each dimension in a convex simplicial polytope.
Book
Introduction to toric varieties
TL;DR: The Geometry and Topology of Singularities course as discussed by the authors was based on a previous course given during the 23o Coloquio Brasileiro de Matematica (Rio de Janeiro, July 2001).
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Kähler-Einstein metrics with positive scalar curvature
TL;DR: In this article, it was shown that the existence of Kahler-Einstein metrics implies the stability of the underlying Kahler manifold in a suitable sense, which disproves a long-standing conjecture that a compact KG admits KG metrics if it has positive first Chern class and no nontrivial holomorphic vector fields.
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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.