Curvature Formulas Related to a Family of Stable Higgs Bundles

@article{Hu2021CurvatureFR,
  title={Curvature Formulas Related to a Family of Stable Higgs Bundles},
  author={Zhi Hu and Pengfei Huang},
  journal={Communications in Mathematical Physics},
  year={2021}
}
  • Zhi Hu, Pengfei Huang
  • Published 29 December 2020
  • Mathematics
  • Communications in Mathematical Physics
Abstract. In this paper, we investigate the geometry of the base complex manifold of an effectively parametrized holomorphic family of stable Higgs bundles over a fixed compact Kähler manifold. The starting point of our study is Schumacher–Toma/Biswas–Schumacher’s curvature formulas for Weil–Petersson-type metrics, in Sect. 2, we give some applications of their formulas on the geometric properties of the base manifold. In Sect. 3, we calculate the curvature on the higher direct image bundle… 

References

SHOWING 1-10 OF 30 REFERENCES

Constructing variations of Hodge structure using Yang-Mills theory and applications to uniformization

The fundamental group is one of the most basic topological invariants of a space. The aim of this paper is to present a method of constructing representations of fundamental groups in complex

Groupe de Picard des variétés de modules de fibrés semi-stables sur les courbes algébriques

Soient X une courbe algebrique projective lisse de genre g ≥ 2 sur ℂ, r, d des entiers, avec r ≥ 2. On note U(r,d) la variete de modules des fibres algebriques semi-stables sur X de rang r et de

Geometry of moduli spaces of Higgs bundles

We construct a Petersson-Weil type Kahler form on the moduli spaces of Higgs bundles over a compact Kahler manifold. A fiber integral formula for this form is proved, from which it follows that the

Positivity of relative canonical bundles and applications

Given a family $f:\mathcal{X} \to S$ of canonically polarized manifolds, the unique Kähler–Einstein metrics on the fibers induce a hermitian metric on the relative canonical bundle

THE SELF-DUALITY EQUATIONS ON A RIEMANN SURFACE

In this paper we shall study a special class of solutions of the self-dual Yang-Mills equations. The original self-duality equations which arose in mathematical physics were defined on Euclidean

Curvature of higher direct image sheaves

Given a family $(F,h) \to X \times S$ of Hermite-Einstein bundles on a compact K\"ahler manifold $(X,g)$ we consider the higher direct image sheaves $R^q p_* \mathcal{O}(F)$ on $S$, where $p: X

Special geometry

Aspecial manifold is an allowed target manifold for the vector multiplets ofD=4,N=2 supergravity. These manifolds are of interest for string theory because the moduli spaces of Calabi-Yau threefolds

Anti Self‐Dual Yang‐Mills Connections Over Complex Algebraic Surfaces and Stable Vector Bundles

On presente une correspondance entre la geometrie algebrique et la geometrie differentielle des fibres vectoriels. Soit une surface algebrique projective X qui a un plongement donne X≤CP N et soit ω