Abstract:

We consider the problem of finding the limit at infinity (corresponding to the downward Morse flow) of a Higgs bundle in the nilpotent cone under the natural C^*-action on the moduli space. For general rank we provide an answer for Higgs bundles with regular nilpotent Higgs field, while in rank three we give the complete answer. Our results show that the limit can be described in terms of data defined by the Higgs field, via a filtration of the underlying vector bundle. At the end of the talk we could discuss the possible connections with non-abelian Hodge Theory and character varieties, most of all because the character variety of the fundamental group of a projective manifold is homeomorphic to the moduli space of semistable Higgs bundles on that manifold.

This is joint work with Peter Gothen (Porto).