arXiv subjects

ZhenYe Li

Publications and source records attributed to ZhenYe Li.

4 recordsLinked to original sources

arXiv2022

Weighted K-stability of $\mathbb Q$-Fano spherical varieties

Let $G$ be a connected, complex reductive Lie group and $X$ a $\mathbb Q$-Fano $G$-spherical variety. In this paper we compute the weighed non-Archimedean functionals of a $G$-equivariant normal test configurations of $X$ via combinatory data. Also we define a modified Futaki invariant with respect to the weight $g$, and give an expression in terms of intersection numbers. Finally we show the equivalence of different notations of stability and gives a stability criterion on $\mathbb Q$-Fano spherical varieties, which is also a criterion of existence of Kähler-Ricci $g$-solitons.

math.DG↗

arXiv2022

Equivariant $\mathbb R$-test configurations and semistable limits of $\mathbb Q$-Fano group compactifications

Let $G$ be a connected, complex reductive group. In this paper, we classify $G\times G$-equivariant normal $\mathbb R$-test configurations of a polarized $G$-compactification. Then for $\mathbb Q$-Fano $G$-compactifications, we express the H-invariant of its equivariant normal $\mathbb R$-test configurations in terms of the combinatory data. Based on \cite{Han-Li}, we compute the semistable limit of a K-unstable Fano $G$-compactification. As an application, we show that for the two K-unstable Fano $SO_4(\mathbb C)$-compactifications, the corresponding semistable limits are indeed the limit spaces of the normalized Kähler-Ricci flow.

math.DG↗

arXiv2020

Kähler-Einstein metrics and Ding functional on $\mathbb Q$-Fano group compactifications

Let $G$ be a complex, connect reductive Lie group which is the complexification of a compact Lie group $K$. Let $M$ be a $\mathbb Q$-Fano $G$-compactification. In this paper, we first prove the uniqueness of $K\times K$-invariant (singular) Kähler-Einstein metric. Then we show the existence of (singular) Kähler-Einstein metric implies properness of the reduced Ding functional. Finally, we show that the barycenter condition is also necessary of properness.

math.DG↗

arXiv2020

Finiteness of $\mathbb Q$-Fano compactifications of semisimple group with Kähler-Einstein metrics

In this note, we give a way to classify $\mathbb Q$-Fano compactifications of a semisimple group $G$. We will prove that there are only finitely many such $\mathbb Q$-Fano $G$-compactifications, which admits (singular) Kähler-Einstein metrics. As an application, this improves a former result in arXiv:2001.11320.

math.DG↗