Chenzi Jin
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View article: Stability thresholds for big classes
Stability thresholds for big classes Open
In 1987, the $α$-invariant theorem gave a fundamental criterion for existence of Kahler-Einstein metrics on smooth Fano manifolds. In 2012, Odaka-Sano extended the framework to $\mathbb{Q}$-Fano varieties in terms of K-stability, and in 20…
View article: A counterexample to Tian's Stabilization Conjecture
A counterexample to Tian's Stabilization Conjecture Open
It was conjectured by Tian that the global log canonical threshold (known as the $α$-invariant) is equal to the level $k$ log canonical threshold (known as the $α_k$-invariant) for all sufficiently large $k$. A weaker folklore conjecture h…
View article: Asymptotics of discrete Okounkov bodies and thresholds
Asymptotics of discrete Okounkov bodies and thresholds Open
This article initiates the study of discrete Okounkov bodies and higher-dimensional Weierstrass gap phenomena, with applications to asymptotic analysis of stability and global log canonical thresholds.
View article: Tian's stabilization problem for toric Fanos
Tian's stabilization problem for toric Fanos Open
In 1988, Tian posed the stabilization problem for equivariant global log canonical thresholds. We solve it in the case of toric Fano manifolds. This is the first general result on Tian's problem. A key new estimate involves expressing comp…
View article: Chebyshev potentials, Fubini–Study metrics, and geometry of the space of Kähler metrics
Chebyshev potentials, Fubini–Study metrics, and geometry of the space of Kähler metrics Open
The Chebyshev potential of a Hermitian metric on an ample line bundle over a projective variety, introduced by Witt Nyström, is a convex function defined on the Okounkov body. It is a generalization of the symplectic potential of a torus‐i…
View article: Chebyshev potentials, Fubini--Study metrics, and geometry of the space of Kähler metrics
Chebyshev potentials, Fubini--Study metrics, and geometry of the space of Kähler metrics Open
The Chebyshev potential of a Kähler potential on a projective variety, introduced by Witt Nyström, is a convex function defined on the Okounkov body. It is a generalization of the symplectic potential of a torus-invariant Kähler potential …