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

• Autorzy: Toshiki Mabuchi
• Języki publikacji: EN

Abstrakty

EN

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 on^X \^X 0, such that [...] whereκ= (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 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]).

• Wydawca: De Gruyter Open
• Czasopismo: Complex Manifolds
• Rocznik: 2016
• Tom: 3
• Numer: 1

Daty

otrzymano

2015-10-10

zaakceptowano

2016-05-03

online

2016-05-12

Twórcy

autor

Toshiki Mabuchi

• Department of Mathematics, Osaka University, Toyonaka, Osaka, 560-0043, Japan

Identyfikatory

DOI

10.1515/coma-2016-0005