Balanced metrics on twisted Higgs bundles

@article{GarciaFernandez2014BalancedMO,
  title={Balanced metrics on twisted Higgs bundles},
  author={Mario Garcia-Fernandez and Julius Ross},
  journal={Mathematische Annalen},
  year={2014},
  volume={367},
  pages={1429-1471}
}
A twisted Higgs bundle on a Kähler manifold X is a pair $$(E,\phi )$$(E,ϕ) consisting of a holomorphic vector bundle E and a holomorphic bundle morphism $$\phi :M \otimes E \rightarrow E$$ϕ:M⊗E→E for some holomorphic vector bundle M. Such objects were first considered by Hitchin when X is a curve and M is the tangent bundle of X, and also by Simpson for higher dimensional base. The Hitchin–Kobayashi correspondence for such pairs states that $$(E,\phi )$$(E,ϕ) is polystable if and only if E… 
The quiver at the bottom of the twisted nilpotent cone on $$\mathbb P^1$$P1
For the moduli space of Higgs bundles on a Riemann surface of positive genus, critical points of the natural Morse–Bott function lie along the nilpotent cone of the Hitchin fibration and are
Quantization of Hitchin's equations for Higgs Bundles I
We provide an algebraic framework for quantization of Hermitian metrics that are solutions of the Hitchin equation for Higgs bundles over a projective manifold. Using Geometric Invariant Theory, we
Quot-scheme limit of Fubini-Study metrics and its applications to balanced metrics
We present some results that complement our prequels [28, 29] on holomorphic vector bundles. We apply the method of the Quotscheme limit of Fubini–Study metrics developed therein to provide a
A deep granular network with adaptive unequal-length granulation strategy for long-term time series forecasting and its industrial applications
TLDR
The experimental results demonstrate that the proposed granular computing (GrC)-based deep learning framework outperforms other data-driven ones on long-term time series forecasting, particularly in an industrial case.

References

SHOWING 1-10 OF 60 REFERENCES
CONSTRUCTING CO-HIGGS BUNDLES ON ℂℙ2
On a complex manifold, a co-Higgs bundle is a holomorphic vector bundle with an endomorphism twisted by the tangent bundle. The notion of generalized holomorphic bundle in Hitchin's generalized
Dimensional reduction and quiver bundles
The so-called Hitchin-Kobayashi correspondence, proved by Donaldson, Uhlenbeck and Yau, establishes that an indecomposable holomorphic vector bundle over a compact Kahler manifold admits a
A Universal Construction for Moduli Spaces of Decorated Vector Bundles over Curves
AbstractLet $X$ be a smooth projective curve over the field of complex numbers, and fix a homogeneous representation $\rho\colon \mathop{\rm GL}(r)\rightarrow \mathop{\rm GL}(V)$. Then one can
Canonical metrics on stable vector bundles
The problem of constructing moduli space of vector bundles over a projective manifold has attracted many mathematicians for decades. In mid 60’s Mumford first constructed the moduli space of vector
On a set of polarized Kähler metrics on algebraic manifolds
A projective algebraic manifold M is a complex manifold in certain projective space CP, N > dim c M = n . The hyperplane line bundle of CP restricts to an ample line bundle L on M. This bundle L is a
Limits of balanced metrics on vector bundles and polarised manifolds
We consider a notion of balanced metrics for triples (X,L,E) which depend on a parameter �, where X is smooth complex manifold with an ample line bundle L and E is a holomorphic vector bundle over X.
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
Moduli space of semistable pairs on a curve
Let X be a smooth projective curve over an algebraically closed field k of any characteristic. A stable pair (E, <p) on X, as defined by Hitchin [2], is a vector bundle E on X together with a
Hitchin–Kobayashi Correspondence, Quivers, and Vortices
Abstract: A twisted quiver bundle is a set of holomorphic vector bundles over a complex manifold, labelled by the vertices of a quiver, linked by a set of morphisms twisted by a fixed collection of
Relative Hitchin–Kobayashi Correspondences for Principal Pairs
A principal pair consists of a holomorphic principal G-bundle together with a holomorphic section of an associated Kaehler fibration. Such objects support natural gauge theoretic equations coming
...
1
2
3
4
5
...