9 citations · 37 across the 9 of their papers we have counts for
9 papers
On Vafa-Witten equations over Kaehler manifolds
Xuemiao Chen
In this paper, we study the analytic properties of solutions to the Vafa-Witten equation over a compact Kaehler manifold. Simple obstructions to the existence of nontrivial solutio…
Admissible Hermitian-Yang-Mills connections over normal varieties
Xuemiao Chen
In this paper, we first prove a complete version of the Donaldson-Uhlenbeck-Yau theorem over normal varieties, including normal Kaehler varieties and projective normal varieties wi…
A Donaldson-Uhlenbeck-Yau theorem for normal varieties and semistable bundles on degenerating families
Xuemiao Chen, Richard A. Wentworth
In this paper, we first prove a Donaldson-Uhlenbeck-Yau theorem over projective normal varieties smooth in codimension two. As a consequence we deduce the polystability of (dual) t…
The nonabelian Hodge correspondence for balanced hermitian metrics of Hodge-Riemann type
Xuemiao Chen, Richard A. Wentworth
This paper extends the nonabelian Hodge correspondence for Kaehler manifolds to a larger class of hermitian metrics on complex manifolds called balanced of Hodge-Riemann type. Esse…
Compactness for -Yang-Mills connections
Xuemiao Chen, Richard A. Wentworth
On a Riemannian manifold of dimension we extend the known analytic results on Yang-Mills connections to the class of connections called -Yang-Mills connections, where is…
Reflexive sheaves, Hermitian-Yang-Mills connections, and tangent cones
Xuemiao Chen, Song Sun
In this paper we give a complete algebro-geometric characterization of analytic tangent cones of admissible Hermitian-Yang-Mills connections over any reflexive sheaves.
Algebraic tangent cones of reflexive sheaves
Xuemiao Chen, Song Sun
We study the notion of algebraic tangent cones at singularities of reflexive sheaves. These correspond to extensions of reflexive sheaves across a negative divisor. We show the exi…
Analytic tangent cones of admissible Hermitian-Yang-Mills connections
Xuemiao Chen, Song Sun
In this paper we study the analytic tangent cones of admissible Hermitian-Yang-Mills connections near a homogeneous singularity of a reflexive sheaf, and relate it to the Harder-Na…
Singularities of Hermitian-Yang-Mills connections and Harder-Narasimhan-Seshadri filtrations
Xuemiao Chen, Song Sun
This is the first of a series of papers where we relate tangent cones of Hermitian-Yang-Mills connections at an isolated singularity to the complex algebraic geometry of the underl…