Branes and moduli spaces of Higgs bundles on smooth projective varieties

Research output: Contribution to journal › Article › Research › peer review

Authors

  • Indranil Biswas
  • Sebastian Heller
  • Laura P. Schaposnik

Research Organisations

External Research Organisations

  • Tata Institute of Fundamental Research (TIFR HYD)
  • University of Illinois at Chicago
View graph of relations

Details

Original languageEnglish
Article number52
JournalRes. Math. Sci.
Volume8
Issue number3
Publication statusPublished - 20 Aug 2021

Abstract

Given a smooth complex projective variety \(M\) and a smooth closed curve \(X \subset M\) such that the homomorphism of fundamental groups \(\pi_1(X) \rightarrow \pi_1(M)\) is surjective, we study the restriction map of Higgs bundles, namely from Higgs bundles on \(M\) to those on \(X\). In particular, we investigate the interplay between this restriction map and various types of branes contained in the moduli spaces of Higgs bundles on \(M\) and \(X\). We also consider the set-up where a finite group is acting on \(M\) via holomorphic automorphisms or anti-holomorphic involutions, and the curve \(X\) is preserved by the action. Branes are studied in this context.

Keywords

    math.AG, math-ph, math.DG, math.MP, math.SG, 14D21, 32L25, 14H70, HyperKähler manifold, Higgs bundle, Connection, Twistor space, Branes

ASJC Scopus subject areas

Cite this

Branes and moduli spaces of Higgs bundles on smooth projective varieties. / Biswas, Indranil; Heller, Sebastian; Schaposnik, Laura P.
In: Res. Math. Sci., Vol. 8, No. 3, 52, 20.08.2021.

Research output: Contribution to journal › Article › Research › peer review

Biswas I, Heller S, Schaposnik LP. Branes and moduli spaces of Higgs bundles on smooth projective varieties. Res. Math. Sci. 2021 Aug 20;8(3):52. doi: 10.48550/arXiv.2005.02564, 10.1007/s40687-021-00286-z
Biswas, Indranil ; Heller, Sebastian ; Schaposnik, Laura P. / Branes and moduli spaces of Higgs bundles on smooth projective varieties. In: Res. Math. Sci. 2021 ; Vol. 8, No. 3.
Download
@article{a710e767e9ed4606a4dac30338bec128,
title = "Branes and moduli spaces of Higgs bundles on smooth projective varieties",
abstract = " Given a smooth complex projective variety \(M\) and a smooth closed curve \(X \subset M\) such that the homomorphism of fundamental groups \(\pi_1(X) \rightarrow \pi_1(M)\) is surjective, we study the restriction map of Higgs bundles, namely from Higgs bundles on \(M\) to those on \(X\). In particular, we investigate the interplay between this restriction map and various types of branes contained in the moduli spaces of Higgs bundles on \(M\) and \(X\). We also consider the set-up where a finite group is acting on \(M\) via holomorphic automorphisms or anti-holomorphic involutions, and the curve \(X\) is preserved by the action. Branes are studied in this context. ",
keywords = "math.AG, math-ph, math.DG, math.MP, math.SG, 14D21, 32L25, 14H70, HyperK{\"a}hler manifold, Higgs bundle, Connection, Twistor space, Branes",
author = "Indranil Biswas and Sebastian Heller and Schaposnik, {Laura P.}",
note = "Funding Information: We thank the two referees for going through the paper very carefully. IB is supported by a J. C. Bose Fellowship. LPS is partially supported by NSF CAREER Award DMS-1749013. On behalf of all authors, the corresponding author states that there is no conflict of interest.",
year = "2021",
month = aug,
day = "20",
doi = "10.48550/arXiv.2005.02564",
language = "English",
volume = "8",
number = "3",

}

Download

TY - JOUR

T1 - Branes and moduli spaces of Higgs bundles on smooth projective varieties

AU - Biswas, Indranil

AU - Heller, Sebastian

AU - Schaposnik, Laura P.

N1 - Funding Information: We thank the two referees for going through the paper very carefully. IB is supported by a J. C. Bose Fellowship. LPS is partially supported by NSF CAREER Award DMS-1749013. On behalf of all authors, the corresponding author states that there is no conflict of interest.

PY - 2021/8/20

Y1 - 2021/8/20

N2 - Given a smooth complex projective variety \(M\) and a smooth closed curve \(X \subset M\) such that the homomorphism of fundamental groups \(\pi_1(X) \rightarrow \pi_1(M)\) is surjective, we study the restriction map of Higgs bundles, namely from Higgs bundles on \(M\) to those on \(X\). In particular, we investigate the interplay between this restriction map and various types of branes contained in the moduli spaces of Higgs bundles on \(M\) and \(X\). We also consider the set-up where a finite group is acting on \(M\) via holomorphic automorphisms or anti-holomorphic involutions, and the curve \(X\) is preserved by the action. Branes are studied in this context.

AB - Given a smooth complex projective variety \(M\) and a smooth closed curve \(X \subset M\) such that the homomorphism of fundamental groups \(\pi_1(X) \rightarrow \pi_1(M)\) is surjective, we study the restriction map of Higgs bundles, namely from Higgs bundles on \(M\) to those on \(X\). In particular, we investigate the interplay between this restriction map and various types of branes contained in the moduli spaces of Higgs bundles on \(M\) and \(X\). We also consider the set-up where a finite group is acting on \(M\) via holomorphic automorphisms or anti-holomorphic involutions, and the curve \(X\) is preserved by the action. Branes are studied in this context.

KW - math.AG

KW - math-ph

KW - math.DG

KW - math.MP

KW - math.SG

KW - 14D21, 32L25, 14H70

KW - HyperKähler manifold

KW - Higgs bundle

KW - Connection

KW - Twistor space

KW - Branes

UR - http://www.scopus.com/inward/record.url?scp=85113181066&partnerID=8YFLogxK

U2 - 10.48550/arXiv.2005.02564

DO - 10.48550/arXiv.2005.02564

M3 - Article

VL - 8

JO - Res. Math. Sci.

JF - Res. Math. Sci.

IS - 3

M1 - 52

ER -