可积系统方法论中的 Schottky 问题及相关问题
代数几何
2026-03-11 v2 可精确求解与可积系统
摘要
本文提供了一种较为非正式的介绍，阐述了可积系统方法论如何应用于 Schottky 问题，解释了雅可比 theta 函数如何用于求解 KP 方程的解，并 culminates于阐述克里赫弗对最退化（弯线）情形下韦尔特斯三切线猜想的证明。
引用
@article{arxiv.2504.20243,
title = {Integrable systems approach to the Schottky problem and related questions},
author = {Samuel Grushevsky and Yuancheng Xie},
journal= {arXiv preprint arXiv:2504.20243},
year = {2026}
}
备注
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