Higgs bundle and local system

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Web6 de nov. de 2008 · Abstract In this paper we study the geometry of the moduli space of (non-strongly) parabolic Higgs bundles over a Riemann surface with marked points. We show that this space possesses a Poisson structure, extending the one on the dual of an Atiyah algebroid over the moduli space of parabolic vector bundles. WebRANK 2 ℓ-ADIC LOCAL SYSTEMS AND HIGGS BUNDLES OVER A CURVE HONGJIE YU Abstract Let X be asmooth, projective,and geometricallyconnected …

On Harder-Narasimhan reductions for Higgs principal bundles

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 … Web24 de jun. de 2012 · We construct five families of 2D moduli spaces of parabolic Higgs bundles (respectively, local systems) by taking the equivariant Hilbert scheme of a certain finite group acting on the cotangent bundle of an elliptic curve (respectively, twisted cotangent bundle). how internet changed our life

An Introduction to the Di erential Geometry of Flat Bundles …

WebIt is true for local systems with complex coefficients. The rough picture is this: A flat connections is equivalent to a local system and the parallel transport of this connection … Weblocal systems and ﬁltered stable degree 0 Higgs bundles over Σ−S. The notion of a ﬁltered Higgs bundle is essentially the same as a Higgs bundle with a quasi-parabolic structure. The notion of a ﬁltered local system is a local system with ﬁltration on each puncture. This correspondence preserves the rank and permutes residue data high heels pain

3 - Representations of surface groups and Higgs bundles

$\\ell$-adic local systems and Higgs bundles: the generic case

WebHiggs 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 … WebHiggs bundles and local systems Simpson, Carlos T. Publications Mathématiques de l'IHÉS, Tome 75 (1992), pp. 5-95. Détail Export Comment citer MR: 94d:32027 Zbl: … high heels paintingWebThe 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, ... local systems. Watch. Notes. Intersection number and systole on hyperbolic surfaces - Tina TORKAMAN, Harvard University (2024-06-21) Let X be a compact … high heels perfect online shop

"WebHiggs bundles on Σ identiﬁes the weight ﬁltration Won the cohomology groups of MB with the perverse ﬁltration Pinduced by the projective Hitchin map on the … " - Higgs bundle and local system

Higgs bundle and local system

Web5 de abr. de 2014 · In this chapter we give an introduction to Higgs bundles and their application to the study of surface group representations. This is based on two fundamental theorems. WebHIGGS BUNDLES AND LOCAL SYSTEMS ON RIEMANN SURFACES RICHARD A. WENTWORTH Contents 1. Preface 1 2. The Dolbeault Moduli Space 3 2.1. Higgs …

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Web17 de fev. de 2014 · Higgs bundles and local systems on Riemann surfaces Authors: Richard Wentworth University of Maryland, College Park Abstract No full-text available ... Web1 de mai. de 2006 · 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 Petersson-Weil form is the curvature of a certain determinant line bundle, equipped with a Quillen metric, on the moduli space of Higgs …

WebHIGGS BUNDLES AND LOCAL SYSTEMS ON RIEMANN SURFACES RICHARD A. WENTWORTH Contents 1. Preface 1 2. The Dolbeault Moduli Space 3 2.1. Higgs … Web7.4 From Flat Bundles to Higgs Bundles 35 7.5 From Higgs Bundles to Flat Bundles 36 7.6 The Case of Line Bundles 36 7.7 Line Bundles: From Flat to Higgs 38 7.8 Line Bundles: From Higgs to Flat 39 8 Examples 42 8.1 Every Riemann Surface is K ahler 42 8.2 Line Bundles over 42 8.3 Some Rank 2 Higgs Bundles 43 8.4 Teichmuller …

Webdetermines both a Higgs bundle (E,ϕ) and a local system L. In fact, it determines a family of λ-connections for all λ∈ C, with the Higgs bundles arising at λ= 0 and the local system, or equivalently a ﬂat connection, at λ= 1. The NAHC (“Kobayashi-Hitchin correspondence” in Mochizuki’s terminology) says that this sets up an ... WebHá 1 dia · -adic local systems and Higgs bundles: the generic case Hongjie Yu Let be a projective smooth geometrically connected curve defined over a finite field of cardinality . Let be a finite set of closed points of . Let and be the base change of , to an algebraic closure.

WebKey words: Higgs bundles; harmonic maps; non-abelian Hodge correspondence. pdf (637 kb) tex (319 kb) ... Wentworth R.A., Higgs bundles and local systems on Riemann …

WebRecall that non-abelian Hodge theory relates two moduli spaces: Local systems (at connections or representations of the fundemental group) on X, and (certain) Higgs bundles on X. The space of Higgs bundles has an action of the group C given by scaling the Higgs eld. Let me recall how the non-abelian Hodge correspondence goes. Suppose … high heels party themeWeb3. S.!Bradlow,!B.!Goldman,!O.!GarcíaEPrada!and!A.!Wienhard,!!Backround!notes!prepared! … how internet comes to indiaWebHilbert Schemes as Moduli of Higgs Bundles and Local Systems Abstract: We construct five families of 2D moduli spaces of parabolic Higgs bundles (respectively, local systems) by taking the equivariant Hilbert scheme of a certain finite group acting on the cotangent bundle of an elliptic curve (respectively, twisted cotangent bundle). how internet comes to sri lankaWebThe Corlette-Donaldson theorem relating the moduli spaces of Higgs bundles and semisim-ple representations of the fundamental group. A description of the oper moduli space and its relationship to systems of holomorphic di erential equations, Higgs bundles, and the Eichler-Shimura isomorphism. Date: March 12, 2012. how internet changed my lifeWebHoje · We are interested in studying the variation of the Hitchin fibration in moduli spaces of parabolic Higgs bundles, under the action of a ramified cover… how internet connection worksWeblocal systems and ﬁltered stable degree 0 Higgs bundles over Σ−S. The notion of a ﬁltered Higgs bundle is essentially the same as a Higgs bundle with a quasi-parabolic … how internet change your lifehttp://www.numdam.org/item/PMIHES_1992__75__5_0/ how internet has changed education