A compactification of the moduli space of principal Higgs bundles over singular curves

Giudice, Alessio Lo; Pustetto, Andrea

doi:10.1016/j.geomphys.2016.08.007

Cited by 3 publications

(3 citation statements)

References 7 publications

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“…Through the work of [163], it was shown in [95] that one can treat a principal G C -Higgs bundle over a nodal curve X as a particular type of vector bundle on the normalization of the curve called a descending bundle, objects which are in one-to-one correspondence with the following singular principal G C -Higgs bundles.…”

Section: Singular Principal G C -Higgs Bundlesmentioning

confidence: 99%

Singular Geometry and Higgs Bundles in String Theory

Anderson¹,

Esole²,

Fredrickson³

et al. 2018

SIGMA

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Abstract. This brief survey aims to set the stage and summarize some of the ideas under discussion at the Workshop on Singular Geometry and Higgs Bundles in String Theory, to be held at the American Institute of Mathematics from October 30th to November 3rd, 2017. One of the most interesting aspects of the duality revolution in string theory is the understanding that gauge fields and matter representations can be described by intersection of branes. Since gauge theory is at the heart of our description of physical interactions, it has opened the door to the geometric engineering of many physical systems, and in particular those involving Higgs bundles. This note presents a curated overview of some current advances and open problems in the area, with no intention of being a complete review of the whole subject.

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Section: Singular Principal G C -Higgs Bundlesmentioning

confidence: 99%

Singular Geometry and Higgs Bundles in String Theory

Anderson¹,

Esole²,

Fredrickson³

et al. 2018

SIGMA

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show abstract

“…and given S ∈ Sch C , M(X, n, L) f unc (S) is the set of isomorphism classes of families of L-twisted semistable principal G-Higgs bundles over the nodal curve X parametrized by S [5]. The authors in [5] also proved that this moduli space M(X, G) is a projective scheme.…”

Section: 1mentioning

confidence: 99%

“…Theorem 2.1 (Theorem 1 in [5]). The moduli space M(X, G, L) is a projective scheme which corepresents the moduli problem M(X, G, L) f unc .…”

Section: 1mentioning

confidence: 99%

Deformation of Locally Free Sheaves and Hitchin Pairs over Nodal Curve

Sun

2019

Preprint

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In this article, we study the deformation theory of locally free sheaves and Hitchin pairs over a nodal curve. As a special case, the infinitesimal deformation of these objects gives the tangent space of the corresponding moduli spaces, which can be used to calculate the dimension of the corresponding moduli space. We show that the deformation of locally free sheaves and Hitchin pairs over a nodal curve is equivalent to the deformation of generalized parabolic bundles and generalized parabolic Hitchin pairs over the normalization of the nodal curve respectively.

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Generalized parabolic structures over smooth curves with many components and principal bundles over reducible nodal curves

Castañeda

2022

Annali di Matematica

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A compactification of the moduli space of principal Higgs bundles over singular curves

Cited by 3 publications

References 7 publications

Singular Geometry and Higgs Bundles in String Theory

Singular Geometry and Higgs Bundles in String Theory

Deformation of Locally Free Sheaves and Hitchin Pairs over Nodal Curve

Generalized parabolic structures over smooth curves with many components and principal bundles over reducible nodal curves

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