Universal Deformation of a Curve and a Differential

Autor:	Carberry, Emma, Schmidt, Martin Ulrich
Rok vydání:	2022
Předmět:	Mathematics - Algebraic Geometry Mathematics - Differential Geometry 14H15
Druh dokumentu:	Working Paper
Popis:	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. Comment: 30 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2211.11442 Zobrazit plný text záznamu View this record from Arxiv