Searcharxiv⌕ Search

arXiv subjects

Yueqiao Wu

Publications and source records attributed to Yueqiao Wu.

7 recordsLinked to original sources
arXiv2026

On polarizations of affine Calabi--Yau varieties

Let $(X, Ω)$ be an affine Calabi--Yau variety, by which we mean a klt affine variety $X$ with a non-vanishing algebraic volume form $Ω$. In connection with complete Calabi--Yau metrics of Euclidean volume growth on $(X, Ω)$, we study algebraic aspects of polarizations of $X$ given by a negative valuation. We show that such a valuation is finitely generated with a klt degeneration if and only if $X$ admits a dlt log Fano type compactification, generalizing a compactification considered by Tian--Yau. We further give a valuative criterion detecting K-semistability of the degeneration by a negative valuation.

math.AG↗
arXiv2026

The space of polarized compactifications of an affine variety

Let $X$ be a normal affine variety over an algebraically closed field of characteristic zero. Through the lens of non-Archimedean geometry, we study the space of polarized compactifications of $X$, consisting of pairs $(\bar X, D)$ where $\bar X$ is a normal projective variety containing $X$ as a dense open subset, and $D$ is an effective ample $\mathbb{Q}$-Cartier $\mathbb{Q}$-divisor with support equal to the complement of $X$ in $\bar X$. We identify this space with a natural class of functions--the Fubini--Study functions--on the Berkovich analytification of $X$. Through a Rees correspondence, we also give a bijection with the space of homogeneous $\mathbb{Q}$-valued, finitely generated negative non-Archimedean norms (or filtrations) on the coordinate ring of $X$. Using the above identifications, we equip the space of polarized compactifications, and numerical classes thereof, with natural metrics and identify the metric completions. The latter include a space of continuous plurisubharmonic functions in the sense of Chambert-Loir and Ducros, and a space of birational curve classes as studied by Dang and Favre.

math.AG↗
arXiv2025

K-semistability of log Fano cone singularities

We give a non-Archimedean characterization of K-semistability of log Fano cone singularities, and show that it agrees with the definition originally defined by Collins--Székelyhidi. As an application, we show that to test K-semistability, it suffices to test special test configurations. We also show that special test configurations give rise to lc places of torus equivariant bounded complements.

math.AG↗
arXiv2024

Some non-Archimedean pluripotential theory on polarized affine cones

We undertake a preliminary step towards studying non-Archimedean pluripotential theory on polarized affine cones over a trivially valued field. We study plurisubharmonic functions and the Monge--Ampère operator defined on the finite energy class, partially generalizing a result of Boucksom--Jonsson on projective varieties.

math.AG↗
arXiv2022

Volume and Monge-Ampère energy on polarized affine varieties

Let $(X, ξ)$ be a polarized affine variety, i.e. an affine variety $X$ with a (possibly irrational) Reeb vector field $ξ$. We define the volume of a filtration of the coordinate ring of $X$ in terms of the asymptotics of the average of jumping numbers. When the filtration is finitely generated, it induces a Fubini-Study function $φ$ on the Berkovich analytification of $X$. In this case, we define the Monge-Ampère energy for $φ$ using the theory of forms and currents on Berkovich spaces developed by Chambert-Loir and Ducros, and show that it agrees with the volume of the filtration. In the special case when the filtration comes from a test configuration, we recover the functional defined by Collins-Székelyhidi and Li-Xu.

math.AG↗
arXiv2021

Boundedness of semistable sheaves

In this expository article, we follow the work of Langer to prove the boundedness of the moduli space of semistable torsion-free sheaves over a projective variety, in any characteristic.

math.AG↗