Degenerations of real normalized differentials (Igor Krichever, Columbia University)

14.10.2019 16:30

The behavior of real-normalized (RN) meromorphic differentials on Riemann surfaces under degeneration is studied. In particular, it is proved that the residues at the nodes are solutions of a suitable Kirchhoff problem on the dual graph of the curve. It is further shown that the limits of zeroes of RN differentials are the divisor of zeroes of a twisted differential --- an explicitly constructed collection of RN differentials on the irreducible components of the stable curve, with higher order poles at some nodes.
Our main tool is a new method for constructing differentials on smooth Riemann surfaces, in a plumbing neighborhood of a given stable curve.

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