Uniqueness of Kähler Ricci shrinkers on toric orbifolds
Yu Li, Wenjia Zhang
Abstract
In this paper, we prove the uniqueness of Kähler Ricci shrinkers on toric orbifolds, extending the corresponding results previously established for toric manifolds.
Table of Contents
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Uniqueness of Kähler Ricci shrinkers on toric orbifolds
Authors
Yu Li, Wenjia Zhang
Abstract
In this paper, we prove the uniqueness of Kähler Ricci shrinkers on toric orbifolds, extending the corresponding results previously established for toric manifolds.
Paper Structure
This paper contains 10 sections, 38 theorems, 109 equations.
Table of Contents
- Introduction
- Symplectic toric orbifolds
- Geometry of orbifolds
- Symplectic toric orbifolds and labeled polyhedra
- Kähler geometry of toric orbifolds
- Kähler metrics on toric orbifolds
- Geometry of Ricci shrinker orbifolds
- Proof of the main theorems
- Kähler Ricci shrinkers on toric orbifolds
- Uniqueness of solutions
Key Result
Theorem 1.1
Suppose $(M^{2n}, J, \mathbb{T}^n)$ is a complex orbifold with an effective and holomorphic $\mathbb{T}^n$-action. Then, up to equivariant biholomorphism, there is at most one $\mathbb{T}^n$-invariant Kähler Ricci shrinker $(M,g, J, f)$ with bounded scalar curvature.
Theorems & Definitions (84)
- Theorem 1.1
- Theorem 1.2
- Definition 2.1: Vector orbispace
- Definition 2.2: Local chart
- Definition 2.3: Smooth orbifolds
- Definition 2.4: Smooth map
- Definition 2.5: Suborbifold
- Definition 2.6: Vector orbibundle
- Definition 2.7: Orbifold fundamental group
- Definition 2.8: Orbifold de Rham cohomology
- ...and 74 more