A criterion for quadraticity of a representation of the fundamental group of an algebraic variety - Archive ouverte HAL Access content directly
Journal Articles Manuscripta mathematica Year : 2017

A criterion for quadraticity of a representation of the fundamental group of an algebraic variety

Louis-Clément Lefèvre

Abstract

Let $\Gamma$ be a finitely presented group and $G$ a linear algebraic group over $\mathbb{R}$. A representation $\rho:\Gamma\rightarrow G(\mathbb{R})$ can be seen as an $\mathbb{R}$-point of the representation variety $\mathfrak{R}(\Gamma, G)$. It is known from the work of Goldman and Millson that if $\Gamma$ is the fundamental group of a compact Kähler manifold and $\rho$ has image contained in a compact subgroup then $\rho$ is analytically defined by homogeneous quadratic equations in $\mathfrak{R}(\Gamma, G)$. When $X$ is a smooth complex algebraic variety, we study a certain criterion under which this same conclusion holds.
Fichier principal
Vignette du fichier
article.pdf (236.32 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-01196355 , version 1 (09-09-2015)

Identifiers

Cite

Louis-Clément Lefèvre. A criterion for quadraticity of a representation of the fundamental group of an algebraic variety. Manuscripta mathematica, 2017, 152 (3-4), pp.381-397. ⟨10.1007/s00229-016-0866-7⟩. ⟨hal-01196355⟩
216 View
152 Download

Altmetric

Share

Gmail Facebook X LinkedIn More