Higgs bundles introduction
WebarXiv: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´ Web5 de jul. de 2001 · Introduction THE primary purpose of this paper is the study of algebraic vector bundles over an elliptic curve (defined over an algebraically closed field k). The interest of the elliptic curve lies… Expand 943 PDF Vanishing theorems for square-integrable harmonic forms J. Dodziuk Mathematics 1981
Higgs bundles introduction
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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 … 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 …
Web30 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 … http://content.algebraicgeometry.nl/2024-3/2024-3-010.pdf
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 … WebAn Introduction to Spectral Data for Higgs Bundles Laura P. Schaposnik Department of Mathematics University of Illinois at Urbana-Champaign IL 61801, USA [email protected] These notes provide an introduction to Higgs bundles for complex and real Lie groups, as well as a description of their associated spectral data. 1. …
Higgs bundles were first introduced by Hitchin in 1987, for the specific case where the holomorphic vector bundle E is over a compact Riemann surface. Further, Hitchin's paper mostly discusses the case where the vector bundle is rank 2 (that is, the fiber is a 2-dimensional vector space). The rank 2 … Ver mais In mathematics, a Higgs bundle is a pair $${\displaystyle (E,\varphi )}$$ consisting of a holomorphic vector bundle E and a Higgs field $${\displaystyle \varphi }$$, a holomorphic 1-form taking values in the bundle of … Ver mais • Hitchin system Ver mais rcrh02beWeb3 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 … simsincorporated.comWebAbstract. I will review the basic concepts of Higgs bundles and the moduli space of Higgs bundles, and then focus the non-Abelian Hodge correspondence: relation between the … rcr flashcardsWebHiggs 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 rcrf taxWebLet D be either the canonical bundle ΩC or a line bundle with deg(D) > 2g − 2 on C. A D-Higgs bundle, or simply Higgs bundle, is a pair (E,φ), where E is a vector bundle on C and φ : E → E ⊗ D is a homomorphism. A Higgs bundle (E,φ) is stable if for every propre subbundle F ⊂ E such that φ induces a homomorphism F → F ⊗ D, we have rcrfrWebAn Introduction to Higgs Bundles via Harmonic Maps Qiongling Li Chern Institute of Mathematics and LPMC, Nankai University, Tianjin 300071, China Received October 16, … rcrg directoryWebWe show that for every nonelementary representation of a surface group into there is a Riemann surface structure such that the Higgs bundle associated to the representation lies outside the discriminant locus of the H… simsimply bathroom shelf