Séance Séminaire

Séminaire Algèbre Géométrie Algébrique Topologie Algébrique

Hodge Theory on Alexander Modules

Alexander modules are the homology groups of certain infinite cyclic covers of complex algebraic varieties, and provide a useful tool in the study of singularities. In the first part of the talk, I will give an overview of Alexander modules, (mixed) Hodge structures, and the main properties of the mixed Hodge structure on Alexander modules defined in joint work with Christian Geske, Moisés Herradón Cueto, Laurentiu Maxim and Botong Wang. In the second part of the talk, we will explore the analogy between Milnor fibers and Alexander modules. The cohomology of a Milnor fiber carries a monodromy action, whose semisimple part is an isomorphism of mixed Hodge structures. We will talk about the generalization of this fact to the world of Alexander modules, as well as about some consequences and explicit computations. Joint work with Moisés Herradón Cueto.