arXiv subjects

Jiyuan Han

Publications and source records attributed to Jiyuan Han.

10 recordsLinked to original sources

arXiv2026

Stable Degenerations of log Fano Fibration Germs

We prove the stable degeneration conjecture of log Fano fibration germs formulated by Sun-Zhang. Precisely, we introduce the $\mathbf{H}$-invariant for filtrations over a log Fano fibration germ, and show that there exists a unique quasi-monomial valuation $v_0$ minimizing the $\mathbf{H}$-invariant. Moreover, we prove that the associated graded ring of $v_0$ is finitely generated and induces a special degeneration to a K-semistable polarized log Fano fibration germ, which further admits a unique K-polystable special degeneration.

math.AG↗

arXiv2025

Variation of Kahler-Einstein metrics with mixed singularities

In this short note, we consider a fiberation f: (X, Delta) to Y between two compact Kahler manifolds with generic fiber of f being a smooth log canonical pair with ample canonical divisor, we prove that the current induced by variation of Kahler Einsteins with mixed cone and Poincare singularities is positive, hence generalize the result of Schumacher in the smooth case [22] and the result of Guenancia in the conic case [14]. As application, we prove the surjectivity of Albanese map for a smooth log canonical pair with -(KX + Delta) being nef.

math.DG↗

arXiv2025

$\mathbb{G}$-uniform weighted K-stability for models on klt varieties

In this paper, we make a generalization of the results in \cite{Li22a} to the singular and weighted setting. In particular, we show that on a polarized projective klt variety, the $\mathbb{G}$-uniform weighted K-stability for models implies the $\mathbb{G}$-coercivity of the weighted Mabuchi functional. In the toric case, we further show that the $(\mathbb{C}^{\times})^n$-uniform $(\mathrm{v},\mathrm{w}\cdot\ell_{\mathrm{ext}})$-weighted K-stability is preserved when perturbing the polarization on the resolution, which implies the existence of the weighted extremal metric(s) on the resolution if the weight function $\mathrm{v}$ is log-concave.

math.DG↗

arXiv2024

On the Existence of Weighted-cscK Metrics

In this paper, we prove that on a smooth K\"ahler manifold, the $\mathbb{G}$-coercivity of the weighted Mabuchi functional implies the existence of the (v, w)-weighted-cscK (extremal) metric with v log-concave (firstly studied in \cite{Lah19}), e.g, cscK metrics, K\"ahler-Ricci solitons, $\mu$-cscK metrics.

math.DG↗

arXiv2023

Superconductivity in pressurized trilayer La$_4$Ni$_3$O$_{10-{\delta}}$ single crystals

The pursuit of discovering new high-temperature superconductors that diverge from the copper-based paradigm1-3 carries profound implications for elucidating mechanisms behind superconductivity and may also enable new applications4-8. Here, our investigation reveals that application of pressure effectively suppresses the spin and charge order in trilayer nickelate La4Ni3O10-{\delta} single crystals, leading to the emergence of superconductivity with a maximum critical temperature (Tc) of around 30 K at 69.0 GPa. The DC susceptibility measurements confirm a substantial diamagnetic response below Tc, indicating the presence of bulk superconductivity with a volume fraction exceeding 80%. In the normal state, we observe a "strange metal" behavior, characterized by a linear temperature-dependent resistance extending up to 300 K. Furthermore, the layer-dependent superconductivity observed hints at a unique interlayer coupling mechanism specific to nickelates, setting them apart from cuprates in this regard. Our findings provide crucial insights into the fundamental mechanisms underpinning superconductivity, while also introducing a new material platform to explore the intricate interplay between the spin/charge order, flat band structures, interlayer coupling, strange metal behavior and high-temperature superconductivity.

cond-mat.supr-con↗

arXiv2020

On the Yau-Tian-Donaldson conjecture for generalized Kähler-Ricci soliton equations

Let $(X, D)$ be a log variety with an effective holomorphic torus action, and $Θ$ be a closed positive $(1,1)$-current. For any smooth positive function $g$ defined on the moment polytope of the torus action, we study the Monge-Ampère equations that correspond to generalized and twisted Kähler-Ricci $g$-solitons. We prove a version of Yau-Tian-Donaldson (YTD) conjecture for these general equations, showing that the existence of solutions is always equivalent to an equivariantly uniform $Θ$-twisted $g$-Ding-stability. When $Θ$ is a current associated to a torus invariant linear system, we further show that equivariant special test configurations suffice for testing the stability. Our results allow arbitrary klt singularities and generalize most of previous results on (uniform) YTD conjecture for (twisted) Kähler-Ricci/Mabuchi solitons or Kähler-Einstein metrics.

math.DG↗

arXiv2020

Algebraic uniqueness of Kähler-Ricci flow limits and optimal degenerations of Fano varieties

We prove that for any $\mathbb{Q}$-Fano variety $X$, the special $\mathbb{R}$-test configuration that minimizes the $H$-functional is unique and has a K-semistable $\mathbb{Q}$-Fano central fibre $(W, ξ)$. Moreover there is a unique K-polystable degeneration of $(W, ξ)$. As an application, we confirm the conjecture of Chen-Sun-Wang about the algebraic-uniqueness for Kähler-Ricci flow limits on Fano manifolds, which implies that the Gromov-Hausdorff limit of the flow does not depend on the choice of initial Kähler metrics. The results are achieved by studying algebraic optimal degeneration problems via new functionals of real valuations, which are analogous to the minimization problem for normalized volumes.

math.AG↗

arXiv2019

Existence and compactness theory for ALE scalar-flat Kähler surfaces

Our main result in this article is a compactness result which states that a noncollapsed sequence of asymptotically locally Euclidean (ALE) scalar-flat Kähler metrics on a minimal Kähler surface whose Kähler classes stay in a compact subset of the interior of the Kähler cone must have a convergent subsequence. As an application, we prove the existence of global moduli spaces of scalar-flat Kähler ALE metrics for several infinite families of Kähler ALE spaces.

math.DG↗

arXiv2018

Local moduli of scalar-flat Kähler ALE surfaces

In this article, we give a survey of our construction of a local moduli space of scalar-flat Kähler ALE metrics in complex dimension $2$. We also prove an explicit formula for the dimension of this moduli space on a scalar-flat Kähler ALE surface which deforms to the minimal resolution of $\mathbb{C}^2/Γ$, where $Γ$ is a finite subgroup of ${\rm{U}}(2)$ without complex reflections, in terms of the embedding dimension of the singularity.

math.DG↗

arXiv2018

Deformation theory of scalar-flat Kähler ALE surfaces

We prove a Kuranishi-type theorem for deformations of complex structures on ALE Kähler surfaces. This is used to prove that for any scalar-flat Kähler ALE surface, all small deformations of complex structure also admit scalar-flat Kähler ALE metrics. A local moduli space of scalar-flat Kähler ALE metrics is then constructed, which is shown to be universal up to small diffeomorphisms (that is, diffeomorphisms which are close to the identity in a suitable sense). A formula for the dimension of the local moduli space is proved in the case of a scalar-flat Kähler ALE surface which deforms to a minimal resolution of $\mathbb{C}^2/Γ$, where $Γ$ is a finite subgroup of ${\rm{U}}(2)$ without complex reflections.

math.DG↗