Asymptotics for general connections at infinity

Carlos T. Simpson

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arXiv · math/0311531

Asymptotics for general connections at infinity

Carlos T. Simpson

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Abstract

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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BibTeX RIS

Carlos T. Simpson. 2003-11-28. Asymptotics for general connections at infinity. https://arxiv.org/abs/math/0311531

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