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The Krichever correspondence for algebraic surfaces. (English. Russian original) Zbl 1078.14525
Funct. Anal. Appl. 35, No. 1, 74-76 (2001); translation from Funkts. Anal. Prilozh. 35, No. 1, 88-90 (2001).
From the text: In the theory of integrable systems, there is a well-known construction due to Krichever, which assigns an infinite-dimensional subspace in the space \(k((z))\) of Laurent power series to algebraic curves and vector bundles on these curves. This construction has numerous applications to integrable systems like the KP equations and to the theory of moduli of algebraic curves. Recently, the author indicated some relations between the KP equations and \(n\)-dimensional local fields. On the basis of these relations, we suggest a generalization of Krichever’s construction to the case of algebraic surfaces.

14H70 Relationships between algebraic curves and integrable systems
14J99 Surfaces and higher-dimensional varieties
37K20 Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions
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