Asymptotics for general connections at infinity

Details Asymptotics for general connections at infinity Asymptotics for general connections at infinity

2003-11-28

arxiv.org/abs/math/0311531v1

Mathematics

Algebraic Geometry

My talk at the Ramis conference, Toulouse, September 2003

Scientific paper

For a standard path of connections going to a generic point at infinity in the moduli space $M_{DR}$ of connections on a compact Riemann surface, we show that the Laplace transform of the family of monodromy matrices has an analytic continuation with locally finite branching. In particular the convex subset representing the exponential growth rate of the monodromy is a polygon, whose vertices are in a subset of points described explicitly in terms of the spectral curve. Unfortunately we don't get any information about the size of the singularities of the Laplace transform, which is why we can't get asymptotic expansions for the monodromy.

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