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

Eyssidieux, 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 -