Corpus ID: 235458165

The nonabelian Hodge correspondence for balanced hermitian metrics of Hodge-Riemann type

@inproceedings{Chen2021TheNH,
  title={The nonabelian Hodge correspondence for balanced hermitian metrics of Hodge-Riemann type},
  author={Xuemiao Chen and R. Wentworth},
  year={2021}
}
This paper extends the nonabelian Hodge correspondence for Kähler manifolds to a larger class of hermitian metrics on complex manifolds called balanced of Hodge-Riemann type. Essentially, it grows out of a few key observations so that the known results, especially the Donaldson-Uhlenbeck-Yau theorem and Corlette’s theorem, can be applied in our setting. Though not necessarily Kähler, we show that the Sampson-Siu Theorem proving that harmonic maps are pluriharmonic remains valid for a slightly… Expand
1 Citations
Compactness for $\Omega$-Yang-Mills connections
On a Riemannian manifold of dimension n we extend the known analytic results on Yang-Mills connections to the class of connections called Ω-Yang-Mills connections, where Ω is a smooth, notExpand

References

SHOWING 1-10 OF 29 REFERENCES
Compact moduli spaces for slope-semistable sheaves
We resolve pathological wall-crossing phenomena for moduli spaces of sheaves on higher-dimensional base manifolds. This is achieved by considering slope-semistability with respect to movable curvesExpand
Fundamental Groups of Compact Kähler Manifolds
Introduction Fibering Kahler manifolds and Kahler groups The de Rham fundamental group $L^2$-cohomology of Kahler groups Existence theorems for harmonic maps Applications of harmonic maps Non-AbelianExpand
Stable Higgs bundles on compact Gauduchon manifolds
Abstract Let M be a compact complex manifold equipped with a Gauduchon metric. If TM is holomorphically trivial, and ( V , θ ) is a stable SL ( r , C ) -Higgs bundle on M, then we show that θ = 0 .Expand
The pseudo-effective cone of a compact K\
We prove that a holomorphic line bundle on a projective manifold is pseudo-effective if and only if its degree on any member of a covering family of curves is non-negative. This is a consequence of aExpand
Hodge theory and complex algebraic geometry
Introduction. Part I. The Topology of Algebraic Varieties: 1. The Lefschetz theorem on hyperplane sections 2. Lefschetz pencils 3. Monodromy 4. The Leray spectral sequence Part II. Variations ofExpand
A Note on the cone of mobile curves
Abstract S. Boucksom, J.-P. Demailly, M. Păun and Th. Peternell proved that the cone of mobile curves ME ( X ) ¯ of a projective complex manifold X is dual to the cone generated by classes ofExpand
The Chern Classes and Kodaira Dimension of a Minimal Variety
This paper deals with a sort of inequality for the first and second Chern classes of normal projective varieties with numerically effective canonical classes (Theorem 1.1); to some extent it is aExpand
The mixed Hodge–Riemann bilinear relations for compact Kähler manifolds
Abstract.We prove the Hodge–Riemann bilinear relations, the hard Lefschetz theorem and the Lefschetz decomposition for compact Kähler manifolds in the mixed situation.
Hodge-Riemann bilinear relations for Schur classes of ample vector bundles
Let $X$ be a $d$ dimensional projective manifold, $E$ be an ample vector bundle on $X$ and $0\le \lambda_N\le \lambda_{N-1} \le \cdots \le \lambda_1 \le \operatorname{rank}(E)$ be a partition ofExpand
Existence d’applications harmoniques tordues à valeurs dans les variétés à courbure négative
We generalize a theorem of Corlette on existence of twisted harmonic maps into a manifold of non-positive curvature. Ce papier fait suite a une suite d'articles [D, C], etudiant les applicationsExpand
...
1
2
3
...