Higgs bundles introduction
Web1 Introduction This paper studies the convergence properties of the gradient flow of the Yang-Mills-Higgs functional on the space of Higgs bundles over a compact Riemann surface, as introduced by Hitchin in [10]. Higgs bundles that minimise this func-tional correspond to solutions of Hitchin’s self-duality equations, which (modulo Web1 de set. de 2007 · Abstract. A Higgs bundle is a holomorphic vector bundle together with a Higgs field. Such objects first emerged twenty years ago in Nigel Hitchin's study of the …
Higgs bundles introduction
Did you know?
Web17 de abr. de 2024 · Higgs bundles were introduced by Hitchin [ 14] in his study of self-dual equations on a Riemann surface, and studied by Simpson [ 27] in his work on non-abelian Hodge theory. Web15 de set. de 2024 · An Introduction to Higgs Bundles via Harmonic Maps Qiongling Li This survey studies equivariant harmonic maps arising from Higgs bundles. We explain …
WebIn this paper, we study the existence of Poisson metrics on flat vector bundles over noncompact Riemannian manifolds and discuss related consequence, specially on the applications in Higgs bundles, towards generalizing… WebHiggs Bundles Peter Gothen Centro de Matem´atica da Universidade do Porto International School on Geometry and Physics: moduli spaces in geometry, topology and physics. Ci …
Web2.2 Moduli of Higgs bundles Usually one would start out with ordinary Higgs bundles, but with an eye to what will come later, we go straight to the parabolic case. Roughly this … WebThis paper is an introduction to the Higgs bundle theory of Hitchin and Simpson and its applications to the study of representations of complex hyperbolic lattices ... Higgs bundles and representations of complex hyperbolic lattices 3 and not locally isomorphic to PSL(2;R) are uniquely determined by .
Web3 de jul. de 2024 · A Higgs bundle on a Riemann surface is a pair consisting of a holomorphic vector bundle together with an endomorphism valued holomorphic one-form, called the Higgs field. Taking the characteristic polynomial of the Higgs field defines the Hitchin map, which is a proper map from the moduli space of Higgs bundles to a vector …
Webℓ-ADIC LOCAL SYSTEMS AND HIGGS BUNDLES 5 Theorem 1.2. Under the condition of the theorem 1.1, there are q-Weil integers αand integers mα such that Eirr n (R) Frob∗k = Pic0 X(Fqk) X α mαα k, ∀k> 1. The αthat appeared in the above equality are monomials in q-Weil numbers of the curve Xand roots of unity.Here q-Weil numbers of the curve Xrefer … costume hoop earringsWebThe non-abelian Hodge theory identifies moduli spaces of representations with moduli spaces of Higgs bundles through solutions to Hitchin's selfduality equations. On the one hand, ... We hope to give a gentle introduction to this theory, and to introduce some modern explorations along this theme. Turning smooth 4-manifolds into maps between ... breastscreen wa perth western australiaWeb27 de ago. de 2024 · The aim is to provide a brief introduction to algebraic stacks, and then to give several constructions of the moduli stack of Higgs bundles on algebraic curves. … breast screen wonthaggiWebbundles is in some sense bounded by the dimension of the manifold. This the-orem can be proved using some simple facts about homotopy and transversality of sections of vector … costume hooves for feethttp://content.algebraicgeometry.nl/2024-3/2024-3-010.pdf costume horn rimmed glassesWeb30 de set. de 2015 · The main purpose is to describe the new discovery of the relation between the following two disparate subjects: one is the topological recursion, that has its origin in random matrix theory and has been effectively applied to many enumerative geometry problems; and the other is the quantization of Hitchin spectral curves … costume hire norwichWebHiggs bundles were introduced by Hitchin in [N1] as solutions of the so-called Hitchin equations, the 2-dimensional reduction of the Yang-Mills self-duality equations, given by where F A is the curvature of a unitary connection ∇A = ∂A + ¯¯ ¯∂A associated to the ¯¯ ¯∂ -connection ¯¯ ¯∂A on a principal GC bundle P . breasts cup