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Higgs bundle and local system

WebClosely related to the theory of Higgs bundles is the theory of local systems (i.e., vector bundles with a flat connection). The works of Hitchin and Simpson [51, 52] have … 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.

Hilbert Schemes as Moduli of Higgs Bundles and Local Systems

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 … Web1 de set. de 2024 · Higgs bundles and local systems Article Dec 1992 Carlos Simpson View Differential Geometry of Complex Vector Bundles Article S. Kobayashi View Twisted Harmonic Maps and the Self-Duality... cryptorecovery.biz reviews https://imperialmediapro.com

W H A T I S . . . a Higgs Bundle? - American Mathematical Society

WebA 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 self-duality equations on a Riemann surface and in Carlos Simp- son’s Ph.D. thesis and subsequent work on nonabelian Hodge theory. 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: … WebA 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 self-duality equations on a … dutch east india company in indonesia

Geometry of moduli spaces of Higgs bundles - Semantic Scholar

Category:VARIATIONS OF HODGE STRUCTURE IN NAHT

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Higgs bundle and local system

VARIATIONS OF HODGE STRUCTURE IN NAHT

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 … Web1 de mai. de 2005 · A. Dey, R. Parthasarathi. Published 1 May 2005. Mathematics. Proceedings of the Indian Academy of Sciences - Mathematical Sciences. The existence and uniqueness of H-N reduction for the Higgs principal bundles over nonsingular projective variety is shown. We also extend the notion of H-N reduction for (Γ,G) …

Higgs bundle and local system

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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 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 on Σ identifies the weight filtration Won the cohomology groups of MB with the perverse filtration Pinduced by the projective Hitchin map on the … 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 …

WebHIGGS BUNDLES AND LOCAL SYSTEMS ON RIEMANN SURFACES RICHARD A. WENTWORTH Contents 1. Preface 1 2. The Dolbeault Moduli Space 3 2.1. Higgs … Web1 de set. de 2007 · 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 self …

Webparabolic Higgs bundles (respectively, local systems), confirming a conjecture of Boalch in these cases and extending a result of Gorsky–Nekrasov–Rubtsov. Using the McKay …

http://www.numdam.org/item/PMIHES_1992__75__5_0/ dutch east india company established inWebRecall 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 … dutch east india company land claimedWeblocal 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 … cryptorealminingWeb28 de dez. de 2016 · Higgs Bundles and Local Systems on Riemann Surfaces. In: Alvarez Consul, L., Andersen, J., Mundet i Riera, I. (eds) Geometry and Quantization of Moduli … cryptorec tlsWebHá 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. dutch east indiaman vliegenthartWebHIGGS BUNDLES AND LOCAL SYSTEMS ON RIEMANN SURFACES RICHARD A. WENTWORTH Contents 1. Preface 1 2. The Dolbeault Moduli Space 3 2.1. Higgs … cryptoregistreWebDol(X,r) for the rigidified moduli space of Higgs bundles (E,q: E !E W1 X) of rank r, together with an isomorphism of a fiber Ex ’Cr. (6) We use M Dol(X,r) for the quotient of R Dol(X,r) by the action of GLr altering the chosen isomorphism. This quotient has geometric points in bijection with polystable Higgs bundles of rank r. Remark1.1 ... cryptorelated puzzle