相关论文: Stable sheaves with twisted sections and the Vafa-…

We consider a version of Hermitian-Einstein equation but perturbed by a Higgs field with a solution called a Donaldson-Thomas instanton on compact K\"ahler threefolds. The equation could be thought of as a generalization of the Hitchin…

On a polarised surface, solutions of the Vafa-Witten equations correspond to certain polystable Higgs pairs. When stability and semistability coincide, the moduli space admits a symmetric obstruction theory and a $\mathbb C^*$ action with…

A `coherent system' $(\Cal E,V)$, consists of a holomorphic bundle plus a linear subspace of its space of holomorphic sections. Based on the usual notion in Geometric Invariant Theory, a notion of slope stability has been defined for such…

We introduce a notion of Gieseker stability for a filtered holomorphic vector bundle $F$ over a projective manifold. We relate it to an analytic condition in terms of hermitian metrics on $F$ coming from a construction of the Geometric…

A twisted Higgs bundle on a K\"ahler manifold $X$ is a pair $(E,\phi)$ consisting of a holomorphic vector bundle $E$ and a holomorphic bundle morphism $\phi\colon M\otimes E \to E$ for some holomorphic vector bundle $M$. Such objects were…

We investigate the set of (real Dolbeault classes of) balanced metrics $\Theta$ on a balanced manifold $X$ with respect to which a torsion-free coherent sheaf $\mathcal{E}$ on $X$ is slope stable. We prove that the set of all such $[\Theta]…

In this paper, we introduce the notions of slope stability and the Hermitian Einstein metric for big cohomology classes. The main result is the Kobayashi Hitchin correspondence on compact normal spaces with big classes admitting the…

In this article, we establish a Hitchin-Kobayashi type correspondence for generalised Seiberg-Witten monopole equations on Kahler surfaces. We show that the "stability" criterion we obtain, for the existence of solutions, coincides with…

We develop a theory of stable bundles and affine Hermitian-Einstein metrics for flat vector bundles over a special affine manifold (a manifold admitting an atlas whose gluing maps are all locally constant volume-preserving affine maps). Our…

The purpose of these notes is to show that the methods introduced by Bauer and Furuta in order to refine the Seiberg-Witten invariants of smooth 4-dimensional manifolds can also be used to obtain stable homotopy classes from Riemann…

We consider the refined $\mathrm{SU}(r)$ Vafa-Witten partition function of a smooth projective surface with non-zero holomorphic 2-form. This partition function has a vertical contribution, expressible in terms of nested Hilbert schemes.…

We adapt the notions of stability of holomorphic vector bundles in the sense of Mumford-Takemoto and Hermitian-Einstein metrics in holomorphic vector bundles for canonically polarized framed manifolds, i.e. compact complex manifolds X…

It is known that given a stable holomorphic pair $(E ,\phi)$, where $E$ is a holomorphic vector bundle on a compact K\"ahler manifold $X$ and $\phi$ is a holomorphic section of $E$, the vector bundle $E$ admits a Hermitian metric solving…

We prove an analogue of the Hitchin-Kobayashi correspondence for compact, oriented, taut Riemannian foliated manifolds with transverse Hermitian structure. In particular, our Hitchin-Kobayashi theorem holds on any compact Sasakian manifold.…

Let $X$ be a compact Gauduchon manifold, and let $E$ and $V_0$ be holomorphic vector bundles over $X$. Suppose that $E$ is stable when considering all subsheaves preserved by a Higgs field $\theta\in H^0($End$(E)\otimes V_0)$. Then a…

We show the existence of Gauduchon metrics on arbitrary compact hermitian varieties, generalizing our previous work on smoothable singularities. These metrics allow us to define the notion of slope stability for torsion-free coherent…

In this paper, we prove \emph{a priori} estimates for some vortex-type equations on compact Riemann surfaces. As applications, we recover existing estimates for the vortex bundle Monge-Amp\`ere equation, prove an existence and uniqueness…

We present a notion of $\Delta$-stability and stability filtration in arbitrary categories which is equivalent to the existence of Harder-Narasimhan (HN) sequences on objects. Indeed it is equivalent to the existence of a zero morphism, a…

We show a strong Hamiltonian stability result for a simpler and larger distance on the Tamarkin category. We also give a stability result with support conditions.

We propose a definition of Vafa-Witten invariants counting semistable Higgs pairs on a polarised surface. We use virtual localisation applied to Mochizuki/Joyce-Song pairs. For $K_S\le0$ we expect our definition coincides with an…