Related papers: Stability for Line Bundles and Deformed Hermitian-…

In this short note, we show that, assuming a conjecture of Arcara and Miles, a line bundle on a smooth complex projective surface admits a deformed Hermitian-Yang-Mills metric if and only if it is stable in the ``large scaling limit" with…

We give an algebraic criterion for the existence of projectively Hermitian-Yang-Mills metrics on a holomorphic vector bundle $E$ over some complete non-compact K\"ahler manifolds $(X,\omega)$, where $X$ is the complement of a divisor in a…

We survey some recent progress on the deformed Hermitian-Yang-Mills (dHYM) equation. We discuss the role of geometric invariant theory (GIT) in approaching the solvability of the dHYM equation, following work of the first author and S.-T.…

This paper begins to study the limiting behavior of a family of Hermitian Yang-Mills (HYM for brevity) metrics on a class of rank two slope stable vector bundles over a product of two elliptic curves with K\"ahler metrics $\omega_\epsilon$…

For $n\geq 3$, let $M$ be an $(n+r)$-dimensional irreducible Hermitian symmetric space of compact type and let $\mathcal{O}_M(1)$ be the ample generator of $Pic(M)$. Let $Y=H_1\cap\dots\cap H_r$ be a smooth complete intersection of…

The deformed Hermitian Yang-Mills (dHYM) equation is a special Lagrangian type condition in complex geometry. It requires the complex analogue of the Lagrangian phase, defined for Chern connections on holomorphic line bundles using a…

Let $(X,\omega)$ be a compact K\"ahler manifold of complex dimension $n$ and $(L,h)$ be a holomorphic line bundle over $X$. The line bundle mean curvature flow was introduced in \cite{JY} in order to find deformed Hermitian-Yang-Mills…

Let $L$ be a holomorphic line bundle over a compact K\"ahler manifold $X$. Motivated by mirror symmetry, we study the deformed Hermitian-Yang-Mills equation on $L$, which is the line bundle analogue of the special Lagrangian equation in the…

We prove that the existence of a $Z$-positive and $Z$-critical Hermitian metric on a rank 2 holomorphic vector bundle over a compact K\"ahler surface implies that the bundle is $Z$-stable. As particular cases, we obtain stability results…

We investigate hermitian Yang-Mills connections on pullback bundles with respect to adiabatic classes on the total space of holomorphic submersions with connected fibres. Under some technical assumptions on the graded object of a…

The deformed Hermitian-Yang-Mills equation is a complex Hessian equation on compact K\"ahler manifolds that corresponds to the special Lagrangian equation in the context of the Strominger-Yau-Zaslow mirror symmetry. Recently, Chen proved…

In this note, we prove that the syzygy bundle $M_L$ is cohomologically stable with respect to $L$ for any ample and globally generated line bundle $L$ on an Enriques (resp. bielliptic) surface over an algebraically closed field of…

Given a line bundle L on a smooth projective curve over the complex numbers, we show that a general extension E of L by the trivial line bundle is very stable: line bundles contained in E have degree much less than half the degree of E.…

For an elliptic surface $q:Y \to \Sigma$, with prescribed singular fibres, Stefan Bauer proved directly via algebraic geometry that the stable bundles over $Y$, whose chern classes are pull backs from $\Sigma$, correspond to the stable…

In this paper, we show that the deformed Hermitian Yang-Mills (dHYM) equation on a rational homogeneous variety, equipped with any invariant K\"{a}hler metric, always admits a solution. In particular, we describe the Lagrangian phase, with…

We study the deformed Hermitian-Yang-Mills (dHYM) equation, which is mirror to the special Lagrangian equation, from the variational point of view via an infinite dimensional GIT problem mirror to Thomas' GIT picture for special…

In this paper, we extend a result of Gao Chen regarding the solvability of the twisted deformed Hermitian Yang-Mills equations on compact K\"ahler manifolds to allow for the twisting function to be non-constant and slightly negative in all…

Considering the so-called Simpson system on smooth projective varieties, defined over an algebraically closed field of characteristic 0, whose canonical bundle is ample, I give another proof the stability of this Higgs bundle, from which…

Let $X$ be a compact, K\"ahler, Calabi-Yau threefold and suppose $X\mapsto \underline{X}\leadsto X_t$ , for $t\in \Delta$, is a conifold transition obtained by contracting finitely many disjoint $(-1,-1)$ curves in $X$ and then smoothing…

We study Yang-Mills connections on holomorphic bundles over complex K\"ahler manifolds of arbitrary dimension, in the spirit of Hitchin's and Simpson's study of flat connections. The space of non-Hermitian Yang-Mills (NHYM) connections has…