Louis-Clément Lefèvre, Lycée Hoche, Versailles: Mixed Hodge Structures on Cohomology Jump Ideals
The formal local ring in the representation variety of Kähler manifolds was first described by Goldman and Millson. Reviewing their arguments, we constructed mixed Hodge structures on these local rings at representations given by the monodromy of variations of mixed Hodge structures and extended this to non-compact varieties. Inside the formal local rings are the cohomology jump ideals, defining locally the locus of representations with dimensions constraints on their cohomology groups. Our goal is now to show that these ideals are sub-mixed Hodge structures.
