Integrable systems approach to the Schottky problem and related questions
arXiv:2504.20243
Abstract
We give a somewhat informal introduction to the integrable systems approach to the Schottky problem, explaining how the theta functions of Jacobians can be used to provide solutions of the KP equation, and culminating with the exposition of Krichever's proof of Welters' trisecant conjecture in the most degenerate (flex line) case.
Lecture notes for a course first given at BIMSA in June 2024. Comments and suggestions very welcome! v2: Added remarks on the approach via the Sato Grassmannian. Final version, to appear in the BIMSA school lecture notes volume