scholarly journals Unramified covers and branes on the Hitchin system

2021 ◽  
Vol 377 ◽  
pp. 107493
Author(s):  
Emilio Franco ◽  
Peter B. Gothen ◽  
André Oliveira ◽  
Ana Peón-Nieto
Keyword(s):  
Hitchin System

scholarly journals Topological mirror symmetry for rank two character varieties of surface groups

2021 ◽  
Author(s):  
Mirko Mauri
Keyword(s):  
Moduli Spaces ◽  
Mirror Symmetry ◽  
Surface Groups ◽  
Character Varieties ◽  
Hitchin System ◽  
Global Topology ◽  
Hodge Numbers

AbstractThe moduli spaces of flat $${\text{SL}}_2$$ SL 2 - and $${\text{PGL}}_2$$ PGL 2 -connections are known to be singular SYZ-mirror partners. We establish the equality of Hodge numbers of their intersection (stringy) cohomology. In rank two, this answers a question raised by Tamás Hausel in Remark 3.30 of “Global topology of the Hitchin system”.

scholarly journals Spectral Curves for the Triple Reduced Product of Coadjoint Orbits for SU(3)

2018 ◽  
pp. 611-622 ◽  
Author(s):  
Jacques Hurtubise ◽  
Lisa Jeffrey ◽  
Steven Rayan ◽  
Paul Selick ◽  
Jonathan Weitsman
Keyword(s):  
Differential Equation ◽  
Higgs Field ◽  
Moment Map ◽  
Circle Action ◽  
Coadjoint Orbits ◽  
Genus Zero ◽  
Spectral Curves ◽  
Hitchin System ◽  
The Moment

This chapter gives an identification of the triple reduced product of three coadjoint orbits in SU(3) with a space of Hitchin pairs over a genus zero curve with three punctures, where the residues of the Higgs field at the punctures are constrained to lie in fixed coadjoint orbits. Using spectral curves for the corresponding Hitchin system, the chapter identifies the moment map for a Hamiltonian circle action on the reduced product. Finally, the chapter makes use of results from Adams, Harnad and Hurtubise to find Darboux coordinates and a differential equation for the Hamiltonian.

scholarly journals DONAGI–MARKMAN CUBIC FOR THE GENERALIZED HITCHIN SYSTEM

2014 ◽  
Vol 25 (02) ◽  
pp. 1450016 ◽  
Author(s):  
UGO BRUZZO ◽  
PETER DALAKOV
Keyword(s):  
Hamiltonian System ◽  
Cotangent Bundle ◽  
Integrable Hamiltonian System ◽  
Maximal Rank ◽  
Symmetric Power ◽  
Period Map ◽  
The Third ◽  
Hitchin System ◽  
Completely Integrable Hamiltonian System ◽  
Symplectic Leaves

Donagi and Markman (1993) have shown that the infinitesimal period map for an algebraic completely integrable Hamiltonian system (ACIHS) is encoded in a section of the third symmetric power of the cotangent bundle to the base of the system. For the ordinary Hitchin system the cubic is given by a formula of Balduzzi and Pantev. We show that the Balduzzi–Pantev formula holds on maximal rank symplectic leaves of the G-generalized Hitchin system.

scholarly journals Complete Integrability of the Parahoric Hitchin System

2018 ◽  
Vol 2019 (21) ◽  
pp. 6499-6528
Author(s):  
David Baraglia ◽  
Masoud Kamgarpour ◽  
Rohith Varma
Keyword(s):  
Integrable System ◽  
Abelian Varieties ◽  
Group Scheme ◽  
Complete Integrability ◽  
Projective Curve ◽  
Nilpotent Cone ◽  
Hitchin System ◽  
Moduli Stack ◽  
Complex Projective ◽  
Complex Projective Curve

Abstract Let $\mathcal {G}$ be a parahoric group scheme over a complex projective curve X of genus greater than one. Let $\mathrm {Bun}_{\mathcal {G}}$ denote the moduli stack of $\mathcal {G}$-torsors on X. We prove several results concerning the Hitchin map on $T^{\ast }\!\mathrm {Bun}_{\mathcal {G}}$. We first show that the parahoric analogue of the global nilpotent cone is isotropic and use this to prove that $\mathrm {Bun}_{\mathcal {G}}$ is “very good” in the sense of Beilinson–Drinfeld. We then prove that the parahoric Hitchin map is a Poisson map whose generic fibres are abelian varieties. Together, these results imply that the parahoric Hitchin map is a completely integrable system.

Hitchin System on Singular Curves

2004 ◽  
Vol 140 (2) ◽  
pp. 1043-1072 ◽  
Author(s):  
D. V. Talalaev ◽  
A. V. Chervov
Keyword(s):  
Hitchin System

On the Hitchin system

1996 ◽  
Vol 85 (3) ◽  
pp. 659-683 ◽  
Author(s):  
Bert van Geemen ◽  
Emma Previato
Keyword(s):  
Hitchin System

scholarly journals Geometric quantization of the Hitchin system

2017 ◽  
Vol 14 (04) ◽  
pp. 1750064 ◽  
Author(s):  
Rukmini Dey
Keyword(s):  
Hilbert Space ◽  
Line Bundle ◽  
Moduli Space ◽  
Geometric Quantization ◽  
Higgs Field ◽  
Hitchin System ◽  
Kähler Form

This paper is about geometric quantization of the Hitchin system. We quantize a Kahler form on the Hitchin moduli space (which is half the first Kahler form defined by Hitchin) by considering the Quillen bundle as the prequantum line bundle and modifying the Quillen metric using the Higgs field so that the curvature is proportional to the Kahler form. We show that this Kahler form is integral and the Quillen bundle descends as a prequantum line bundle on the moduli space. It is holomorphic and hence one can take holomorphic square integrable sections as the Hilbert space of quantization of the Hitchin moduli space.

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