# Variations of mixed Hodge structure attached to the deformation theory of a complex variation of Hodge structures

Philippe Eyssidieux; Carlos Simpson

Journal of the European Mathematical Society (2011)

- Volume: 013, Issue: 6, page 1769-1798
- ISSN: 1435-9855

## Access Full Article

top## Abstract

top## How to cite

topEyssidieux, Philippe, and Simpson, Carlos. "Variations of mixed Hodge structure attached to the deformation theory of a complex variation of Hodge structures." Journal of the European Mathematical Society 013.6 (2011): 1769-1798. <http://eudml.org/doc/277766>.

@article{Eyssidieux2011,

abstract = {Let $X$ be a compact Kähler manifold, $x\in X$ be a base point and $\rho :\pi _1(X,x)\rightarrow GL_N(C)$ be the monodromy representation of a $\mathcal \{C\}$-VHS. Building on Goldman–Millson’s classical
work, we construct a mixed Hodge structure on the complete local ring of the representation variety at $\rho $ and a variation of mixed Hodge structures whose monodromy is the universal deformation of $\rho $.},

author = {Eyssidieux, Philippe, Simpson, Carlos},

journal = {Journal of the European Mathematical Society},

keywords = {Kähler manifolds; local systems; mixed Hodge theory; variation of mixed Hodge structure; variety of representations; Kähler manifolds; local systems; mixed Hodge theory; variation of mixed Hodge structure; variety of representations},

language = {eng},

number = {6},

pages = {1769-1798},

publisher = {European Mathematical Society Publishing House},

title = {Variations of mixed Hodge structure attached to the deformation theory of a complex variation of Hodge structures},

url = {http://eudml.org/doc/277766},

volume = {013},

year = {2011},

}

TY - JOUR

AU - Eyssidieux, Philippe

AU - Simpson, Carlos

TI - Variations of mixed Hodge structure attached to the deformation theory of a complex variation of Hodge structures

JO - Journal of the European Mathematical Society

PY - 2011

PB - European Mathematical Society Publishing House

VL - 013

IS - 6

SP - 1769

EP - 1798

AB - Let $X$ be a compact Kähler manifold, $x\in X$ be a base point and $\rho :\pi _1(X,x)\rightarrow GL_N(C)$ be the monodromy representation of a $\mathcal {C}$-VHS. Building on Goldman–Millson’s classical
work, we construct a mixed Hodge structure on the complete local ring of the representation variety at $\rho $ and a variation of mixed Hodge structures whose monodromy is the universal deformation of $\rho $.

LA - eng

KW - Kähler manifolds; local systems; mixed Hodge theory; variation of mixed Hodge structure; variety of representations; Kähler manifolds; local systems; mixed Hodge theory; variation of mixed Hodge structure; variety of representations

UR - http://eudml.org/doc/277766

ER -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.