The moduli and the global period mapping of surfaces with : a counterexample to the global Torelli problem
The Picard group of a primary Kodaira surface.
The Shafarevich-Tate Conjecture for Pencils of Elliptic Curves on K3 Surfaces.
The Soliton-Ricci Flow with variable volume forms
We introduce a flow of Riemannian metrics and positive volume forms over compact oriented manifolds whose formal limit is a shrinking Ricci soliton. The case of a fixed volume form has been considered in our previouswork.We still call this new flow, the Soliton-Ricci flow. It corresponds to a forward Ricci type flow up to a gauge transformation. This gauge is generated by the gradient of the density of the volumes. The new Soliton-Ricci flow exist for all times. It represents the gradient flow of...
The Torelli map at the boundary of the Schottky space.
Theta functions on -bundles over with the zero Euler class.
Theta functions on the Kodaira-Thurston manifold.
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 .
Torelli theorems for Kähler K3 surfaces