Linsheng Wang

activity

20212026

collaborators

9 papers

math.AG2026

Stable Degenerations of log Fano Fibration Germs

Jiyuan Han, Minghao Miao, Lu Qi +2

We prove the stable degeneration conjecture of log Fano fibration germs formulated by Sun-Zhang. Precisely, we introduce the $H$ -invariant for filtrations over a log Fano…

math.AG2025

K-polystability and reduced uniform K-stability of log Fano cone singularities

Linsheng Wang

We prove that a log Fano cone $(X, Δ, ξ_{0})$ satisfying $δ_{T} (X, Δ, ξ_{0}) \geq 1$ is K-polystable for normal test configurations if and only if it is K-polystable for special test…

math.AG2024

Generalized optimal degenerations of Fano varieties

Linsheng Wang

We prove a generalization of the algebraic version of Tian conjecture. Precisely, for any smooth strictly increasing function $g : R \to R_{> 0}$ with ${\rm log}\circ…

math.AG2024

A valuative criterion of K-polystability

Linsheng Wang

For any log Fano pair with a torus action, we associate a computable invariant to it, such that the pair is (weighted) K-polystable if and only if this invariant is greater than on…

math.AG2024

K-stability of special Gushel-Mukai manifolds

Yuchen Liu, Linsheng Wang

Gushel-Mukai manifolds are specific families of $n$ -dimensional Fano manifolds of Picard rank $1$ and index $n - 2$ where $3 \leq n \leq 6$ . A Gushel-Mukai $n$ -fold is either ordinary…

math.AG2024

Optimal Degenerations of K-unstable Fano threefolds

Minghao Miao, Linsheng Wang

We explicitly determine the optimal degenerations of Fano threefolds $X$ in family No 2.23 of Mori-Mukai's list as predicted by the Hamilton-Tian conjecture. More precisely, we fin…

math.AG2023

Kähler-Ricci solitons on Fano threefolds with non-trivial moduli

Minghao Miao, Linsheng Wang

We find Fano threefolds $X$ admitting Kähler-Ricci solitons (KRS) with non-trivial moduli, which are $T$ -varieties of complexity two. More precisely, we show that the weig…

math.CV2023

Bergman kernels on degenerations

Linsheng Wang, Shengxuan Zhou

We introduce the fiberwise Bergman kernel for a flat family of polarized varieties over a Riemann surface, which extends the classical Bergman kernel defined on the reduced fibers.…

math.AG2021

Dimension four simply connected Voisin manifolds

Linsheng Wang

Voisin constructed a series of examples concerning simply connected compact Kähler manifolds of even dimensions, which do not have the rational homotopy type of a complex projectiv…