论文标题
曲线和差异的普遍变形
Universal Deformation of a Curve and a Differential
论文作者
论文摘要
我们为由紧凑的复合曲线和meromormormormormormormormormormormormormormorphic 1形成的对构建了通用的局部变形（Kuranishi家族）。 假定每对是局部平面的，这种情况尤其迫使局部变形保留下属差异的周期。高纤维化病例可为可集成系统的光谱数据（例如KDV方程的简单周期溶液或SINH-GORDON方程（恒定平均曲率的圆柱体））产生通用的局部变形。这是两篇论文中的第一篇，其中我们将开发出可集成系统的光谱曲线数据的变形理论。
We construct a universal local deformation (Kuranishi family) for pairs consisting of a compact complex curve and a meromorphic 1-form. Each pair is assumed to be locally planar, a condition which in particular forces the periods of the meromorphic differential to be preserved by local deformations. The hyperelliptic case yields a universal local deformation for the spectral data of integrable systems such as simply-periodic solutions of the KdV equation or of the sinh-Gordon equation (cylinders of constant mean curvature). This is the first of two papers in which we shall develop a deformation theory of the spectral curve data of an integrable system.
