Higgs bundles introduction
WebThe study of Higgs bundles on curves has been initiated by Hitchin [ 28] in relation to the construction of solutions to a dimensional reduction of the Yang–Mills equation. An essential device to study Higgs bundles has been the Hitchin map, which associates to a pair ( E, θ ), the characteristic polynomial of the Higgs field θ. WebHiggs Bundles - Yale University
Higgs bundles introduction
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Webometry, Higgs bundles. Mathematical Subject Classificication 14G22, 14H60, 14F35 Contents 1. ... Introduction Inthecomplex case, Simpson correspondence generalizes theclassical Narasimhan- Web4 de mar. de 2024 · The terms Higgs field, respectively Higgs bundle were coined by Hitchin and Simpson. This terminology indicates the formal analogy of this geometric …
Web1 de dez. de 2013 · These objects are important because they provide a common generalization of several notions of bundles with structure; indeed principal bundles, … WebThe 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 ...
Web15 de set. de 2024 · An Introduction to Higgs Bundles via Harmonic Maps. These notes are an extended version of lecture notes prepared for the 3-hour mini-course "An … Web27 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. The first construction is via a "bootstrap" method from the algebraic stack of vector bundles on an algebraic curve.
WebThe study of Higgs bundles on curves has been initiated by Hitchin in relation to the construction of solutions to a dimensional reduction of the Yang–Mills equation. An …
WebHIGGS BUNDLES SOURAV DAS Abstract In a recent paper [3], a semi-stable degeneration of modulispace ofHiggs bundles on a curve has been constructed.Inthispaper,weshowthatthereisarelativelog-symplecticformonthisdegeneration,whose restriction to the generic fibre is the classical … citus postgres windowsWebAn Introduction to Higgs Bundles via Harmonic Maps Qiongling Li Chern Institute of Mathematics and LPMC, Nankai University, Tianjin 300071, China Received October 16, … dickson city erWeb1 Introduction The aim of this article is to extend the Donaldson-Corlette-Hitchin-Simpson correspondence between Higgs bundles and flat connections on compact Kähler manifolds to the class of compact quasi-regular Sasakian manifolds. citus indoor ceramic heaterWebℓ-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 … dickson city dicks sporting goodsWebHiggs bundles were introduced by Nigel Hitchin in 1987 while studying the dimensional reduction of the self-duality equations from four to two dimensions. A Higgs bundle on a Riemann surface is a pair (E;), where E is a holomorphic vector bundle and , the Higgs eld, is a holomorphic 1-form with values in the bundle of endomorphisms of E. It dickson city escape roomWebarXiv:math/0610301v2 [math.AG] 12 Oct 2006 ALGEBRAIC NAHM TRANSFORM FOR PARABOLIC HIGGS BUNDLES ON P1 by Kurs¸at Aker¨ Feza Gursey Institute¨ Istanbul, Turkey & Szilard Szab´ dickson city fire companyWeb1 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 citus shard_replication_factor