Time: 14:30
Speaker: Francois-Xavier Machu (Western)
Title: "Monodromy of a class of logarithmic connections over an elliptic curve and local structure of the moduli space of connections"
Room: MC 108

Abstract: The study of the relations between various moduli spaces arising from connections on vector bundles over algebraic varieties is an interesting topic. The most intriguing question is the relation between the moduli space of connections and that of the underlying vector bundles. We illustrate this concept in considering a familly of rank 2 logarithmic connections over an elliptic curve. These rank 2 logarithmic connections are obtained as direct images of regular connections on line bundles over genus-2 double covers of the elliptic curve. We provide an explicit parameterization of all such connections and determine their monodromy and differential Galois group. We address the local structure of the moduli space of connections and give an example of a moduli space of connections having a singularity. This singularity is solved by means of the toric geometry. I will finish this talk in saying a few words on what happens while one considers the genus-1 singular curves.