Stable Higgs \(G\)-sheaves
type: Item
instance of: scholarly article
title: Stable Higgs \(G\)-sheaves
zbMATH Open document ID: 1155.14010
DOI: 10.4171/RMI/553
author: Tomas L. Gómez
author: Ignacio Sols
published in: Revista Matemática Iberoamericana
publication date: 2008-11-05T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.rmi/1218475360
full work available at URL: https://eudml.org/doc/42392
review text: A Higgs bundle over a projective scheme \(X\) is a vector bundle \(E\), together with a homomorphism \(\theta: E\to E\otimes\Omega_X\), such that \(\theta\wedge\theta=0\). The authors extend this notion of Higgs bundles to principal \(G\)-sheaves on a smooth projective complex scheme \(X\) of any dimension, where \(G\) is an arbitrary reductive structure group. The starting point is a principal \(G\)-sheaf \(P\) over a torsion free sheaf \(E\). The authors define a \(G\)-Higgs field on \(P\) by means of a homomorphism \(\Theta:E\oplus(\zeta \otimes \mathcal O_X)\), where \(\zeta\) is the center. Then the authors define the wedge product \(\Theta\wedge\Theta\) by extending sections arising from a natural exact sequence. Higgs \(G\)-sheaves are \(G\)-sheaves for which \(\Theta\wedge\Theta=0\). The notion of semistability for Higgs \(G\)-fields is introduced by means of compatibility with orthogonal algebra filtrations on \(E\). The authors prove the existence of a quasi-projective coarse moduli space of classes of semistable Higgs \(G\)-sheaves, with fixed numerical invariants.
reviewed by: Luca Chiantini
Mathematics Subject Classification ID: 14D22
Mathematics Subject Classification ID: 14D20
zbMATH DE Number: 5361880
zbMATH Keywords: Higgs bundles
MaRDI profile type: Publication
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OpenAlex ID: W1991785707
description: scientific article; zbMATH DE number 5361880