The class ... is not stable by small deformations.
The complex structure on a connected sum of S³ x S³ with trivial canonical bundle.
The graded Lie algebra of a Kähler group.
The pro-unipotent radical of the pro-algebraic fundamental group of a compact Kähler manifold
The aim of this paper is to study the pro-algebraic fundamental group of a compact Kähler manifold. Following work by Simpson, the structure of this group’s pro-reductive quotient is already well understood. We show that Hodge-theoretic methods can also be used to establish that the pro-unipotent radical is quadratically presented. This generalises both Deligne et al.’s result on the de Rham fundamental group, and Goldman and Millson’s result on deforming representations of Kähler groups, and can...
Three-manifolds and Kähler groups
We give a simple proof of a result originally due to Dimca and Suciu: a group that is both Kähler and the fundamental group of a closed three-manifold is finite. We also prove that a group that is both the fundamental group of a closed three-manifold and of a non-Kähler compact complex surface is or .
Towards a Mori theory on compact Kähler threefolds III
Based on the results of the first two parts to this paper, we prove that the canonical bundle of a minimal Kähler threefold (i.e. is nef) is good,i.e.its Kodaira dimension equals the numerical Kodaira dimension, (in particular some multiple of is generated by global sections); unless is simple. “Simple“ means that there is no compact subvariety through the very general point of and not Kummer. Moreover we show that a compact Kähler threefold with only terminal singularities whose canonical...