Qiongling Li

Asymptotics of certain families of Higgs bundles in the Hitchin component

Publication: Research - peer-reviewJournal article

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Asymptotics of certain families of Higgs bundles in the Hitchin component. / Collier, Brian; Li, Qiongling.

In: Advances in Mathematics, Vol. 307, 02.2017.

Publication: Research - peer-reviewJournal article

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Collier, Brian; Li, Qiongling / Asymptotics of certain families of Higgs bundles in the Hitchin component.

In: Advances in Mathematics, Vol. 307, 02.2017.

Publication: Research - peer-reviewJournal article

Bibtex

@article{ee88fa9838ae49ddb49e377f704acb68,
title = "Asymptotics of certain families of Higgs bundles in the Hitchin component",
keywords = "math.DG, math.AG",
author = "Brian Collier and Qiongling Li",
note = "48 pages, v2: ~20 pages added to v1, substantial changes were made to the proof of parallel transport asymptotics",
year = "2017",
month = "2",
volume = "307",
journal = "Advances in Mathematics",

}

RIS

TY - JOUR

T1 - Asymptotics of certain families of Higgs bundles in the Hitchin component

AU - Collier,Brian

AU - Li,Qiongling

N1 - 48 pages, v2: ~20 pages added to v1, substantial changes were made to the proof of parallel transport asymptotics

PY - 2017/2

Y1 - 2017/2

N2 - Using Hitchin's parameterization of the Hitchin-Teichm\"uller component of the $SL(n,\mathbb{R})$ representation variety, we study the asymptotics of certain families of representations. In fact, for certain Higgs bundles in the $SL(n,\mathbb{R})$-Hitchin component, we study the asymptotics of the Hermitian metric solving the Higgs bundle equations. This analysis is used to estimate the asymptotics of the corresponding family of flat connections as we scale the differentials by a real parameter. We consider Higgs fields that have only one holomorphic differential $q_n$ of degree $n$ or $q_{n-1}$ of degree $n-1.$ We also study the asymptotics of the associated family of equivariant harmonic maps to the symmetric space $SL(n,\mathbb{R})/SO(n,\mathbb{R})$ and relate it to recent work of Katzarkov, Noll, Pandit and Simpson.

AB - Using Hitchin's parameterization of the Hitchin-Teichm\"uller component of the $SL(n,\mathbb{R})$ representation variety, we study the asymptotics of certain families of representations. In fact, for certain Higgs bundles in the $SL(n,\mathbb{R})$-Hitchin component, we study the asymptotics of the Hermitian metric solving the Higgs bundle equations. This analysis is used to estimate the asymptotics of the corresponding family of flat connections as we scale the differentials by a real parameter. We consider Higgs fields that have only one holomorphic differential $q_n$ of degree $n$ or $q_{n-1}$ of degree $n-1.$ We also study the asymptotics of the associated family of equivariant harmonic maps to the symmetric space $SL(n,\mathbb{R})/SO(n,\mathbb{R})$ and relate it to recent work of Katzarkov, Noll, Pandit and Simpson.

KW - math.DG

KW - math.AG

M3 - Tidsskriftartikel

VL - 307

JO - Advances in Mathematics

T2 - Advances in Mathematics

JF - Advances in Mathematics

ER -