Higgs bundle and local system

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August undefined, 2024

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 … http://www.numdam.org/item/PMIHES_1992__75__5_0/

Hitchin fibration under ramified coverings - ScienceDirect

WebMelting faces. Blowing minds. Cerebral jams for the masses. SoCal's own jamband, The Higgs 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, ... local systems. Watch. Notes. Intersection number and systole on hyperbolic surfaces - Tina TORKAMAN, Harvard University (2024-06-21) Let X be a compact … how many hundredths are in 0.1

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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 … 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. 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. how many hundredths are in 0.2

(PDF) What is ⋯ a Higgs bundle? - ResearchGate

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Web18 de fev. de 2014 · Higgs bundles and local systems on Riemann surfaces. Lecture notes from the Third International School on Geometry and Physics at the Centre de … 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 ... howard berg obituaryWebHoje · 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 many hundredths are in 1 whole

"WebHoje · Abstract. We are interested in studying the variation of the Hitchin fibration in moduli spaces of parabolic Higgs bundles, under the action of a ramified covering. Given a degree two map π: Y → X between compact Riemann surfaces, we may pull back a Higgs bundle from X to Y, the lifted Higgs bundle tends to have many apparent singularities ... " - Higgs bundle and local system

Higgs bundle and local system

DirectImagesinNonAbelianHodgeTheory arXiv:1612.06388v1 …

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 Web30 de jan. de 2024 · Rank 2. -adic local systems and Higgs bundles over a curve. Hongjie Yu. Let be a smooth, projective, and geometrically connected curve defined over a finite …

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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) … 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 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 … Webrelates meromorphic Higgs bundles and ﬁltered Stokes local systems on curves by taking G = GLn(C). Secondly, due to the lack of a construction of the corresponding moduli spaces, the main result in this paper is only given for categories. Despite this, the Dolbeault and de Rham moduli spaces can be constructed similarly as [20].

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. 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 …

WebWe 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 …

WebHIGGS BUNDLES AND LOCAL SYSTEMS ON RIEMANN SURFACES RICHARD A. WENTWORTH Contents 1. Preface 1 2. The Dolbeault Moduli Space 3 2.1. Higgs … howard berger gorilla planet of the apes 2001WebHá 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 . … howard berger space heaterWeb17 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 ... how many hundredths does it take to make oneWebHiggs 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: … howard berger co space heaterWebHiggs 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 … howard berger space heater cz285Web1 de out. de 1996 · Precisely which parabolic bundles occur in stable K (D) pairs and stable Higgs bundles is determined. Using Morse theory, the moduli space of parabolic Higgs bundles is shown to be a non-compact, connected, simply connected manifold, and a computation of its Poincare polynomial is given. View PDF on arXiv Save to Library … how many hundredths are there in 650Web1 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-duality equations on a Riemann... howard berglas esq