Analyticity of the closures of some Hodge theoretic subspaces

In this paper, we prove a general theorem concerning the analyticity of the closure of a subspace defined by a family of variations of mixed Hodge structures, which includes the analyticity of the zero loci of degenerating normal functions. For the proof, we use a moduli of the valuative version of log mixed Hodge structures

Moduli of log mixed Hodge structures

We announce the construction of toroidal partial compactifications of the moduli spaces of mixed Hodge structures with polarized graded quotients. They are moduli spaces of log mixed Hodge structures with polarized graded quotients. We include an application to the analyticity of zero loci of some functions

Extended period domains, algebraic groups, and higher Albanese manifolds

Advanced lectures in mathematics, 3

Log intermediate Jacobians

We study the degenerations of intermediate Jacobians by means of log geometry. We extend the family of intermediate Jacobians over a punctured disc to a "log intermediate Jacobian" over a disc

On log motives

First published in Tunisian Journal of Mathematics in Vol. 2 (2020), No. 4, published by Mathematical Sciences Publishers