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

Toshiki Mabuchi. "An ℓ-th root of a test configuration of exponent ℓ." Complex Manifolds 3.1 (2016): 169-185. <http://eudml.org/doc/277104>.

@article{ToshikiMabuchi2016,
abstract = {Let (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 onX X̂ 0, such that [...] whereκ= (Y, Q, η) is a test configuration for (X, L) of exponent 1, and D is an effective Q-divisor onX such that ℓD is an integral divisor with support in the fiber X0. Then (κ, D) can be chosen in such a way that [...] where 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]).},
author = {Toshiki Mabuchi},
journal = {Complex Manifolds},
keywords = {polarized algebraic manifold; desingularizations; test configurations},
language = {eng},
number = {1},
pages = {169-185},
title = {An ℓ-th root of a test configuration of exponent ℓ},
url = {http://eudml.org/doc/277104},
volume = {3},
year = {2016},
}

TY - JOUR
AU - Toshiki Mabuchi
TI - An ℓ-th root of a test configuration of exponent ℓ
JO - Complex Manifolds
PY - 2016
VL - 3
IS - 1
SP - 169
EP - 185
AB - Let (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 onX X̂ 0, such that [...] whereκ= (Y, Q, η) is a test configuration for (X, L) of exponent 1, and D is an effective Q-divisor onX such that ℓD is an integral divisor with support in the fiber X0. Then (κ, D) can be chosen in such a way that [...] where 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]).
LA - eng
KW - polarized algebraic manifold; desingularizations; test configurations
UR - http://eudml.org/doc/277104
ER -