Generalized Weierstrass \(\wp\)-functions and KP flows in affine space
The Jacobian of a genus g hyperelliptic curve outside a theta divisor is explicitly isomorphic to an affine subvariety of \({\mathbb{C}}^{3g+1}\) [\textit{C. G. T. Jacobi}, J. Reine Angew. Math. 32, 220-226 (1846); cf. \textit{D. Mumford}, ``Tata lectures on theta. II: Jacobian theta functions and differential equations'', Prog. Math. 43 (1984; Zbl 0549.14014)]. This paper presents an analogous construction for general curves. The construction uses the interpretation of a generic line-bundle as a commutative ring of differential operators and is thus suited to a solution of the KP equation.
Jacobian of a genus g hyperelliptic curve
scientific article; zbMATH DE number 4040083