scholarly journals On the topology of the moduli space of negative constant scalar curvature metrics on a Haken manifold

1999 ◽  
Vol 75 (7) ◽  
pp. 126-128 ◽  
Author(s):  
Minyo Katagiri
Keyword(s):  
Scalar Curvature ◽  
Moduli Space ◽  
Constant Scalar Curvature ◽  
Negative Constant ◽  
Constant Scalar Curvature Metrics

scholarly journals An ℓ-th root of a test configuration of exponent ℓ

2016 ◽  
Vol 3 (1) ◽  
Author(s):  
Toshiki Mabuchi
Keyword(s):  
Scalar Curvature ◽  
Moduli Space ◽  
Constant Scalar Curvature ◽  
Algebraic Manifold ◽  
Positive Real ◽  
Kähler Metrics ◽  
Test Configuration ◽  
Kahler Metrics ◽  
Integral Divisor

AbstractLet (X, L) be a polarized algebraic manifold. Then for every test configuration μ = (X, L,Ψ) for (X, L) of exponent ℓ, we obtain an ℓ-th root (κ, D) of μ and Gm-equivariant desingularizations ι : ^X → X and η : ^X → Y, both isomorphic on^X \^X 0, such thatwhereκ= (Y, Q, η) is a test configuration for (X, L) of exponent 1, and D is an effective Q-divisor on^X such that ℓD is an integral divisor with support in the fiber X0. Then (κ, D) can be chosen in such a way thatwhere C1 and C2 are positive real constants independent of the choice of μ and ℓ. This plays an important role in our forthcoming papers on the existence of constant scalar curvature Kähler metrics (cf. [6]) and also on the compactified moduli space of test configurations (cf. [5],[7]).

scholarly journals Refined asymptotics for constant scalar curvature metrics with isolated singularities

1999 ◽  
Vol 135 (2) ◽  
pp. 233-272 ◽  
Author(s):  
Nick Korevaar ◽  
Rafe Mazzeo ◽  
Frank Pacard ◽  
Richard Schoen
Keyword(s):  
Scalar Curvature ◽  
Constant Scalar Curvature ◽  
Isolated Singularities ◽  
Constant Scalar Curvature Metrics
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