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Connections on the total Picard sheaf and the KP hierarchy

Connections on the total Picard sheaf and the KP hierarchy A family of connections is introduced on a direct limit of Poincaré sheaves of a curve. These connections descend to connections on the corresponding direct limit of Picard sheaves, defined globally on the Jacobian of the curve. All such connections are classified; in particular they are all flat. Krichever's algebro-geometric solutions of the KP equations are recovered upon trivializing the resulting \tdD-modules over the complement of the Θ divisor. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Applicandae Mathematicae Springer Journals

Connections on the total Picard sheaf and the KP hierarchy

Acta Applicandae Mathematicae , Volume 42 (3) – Jul 1, 2004

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References (13)

Publisher
Springer Journals
Copyright
Copyright
Subject
Mathematics; Computational Mathematics and Numerical Analysis; Applications of Mathematics; Partial Differential Equations; Probability Theory and Stochastic Processes; Calculus of Variations and Optimal Control; Optimization
ISSN
0167-8019
eISSN
1572-9036
DOI
10.1007/BF01064170
Publisher site
See Article on Publisher Site

Abstract

A family of connections is introduced on a direct limit of Poincaré sheaves of a curve. These connections descend to connections on the corresponding direct limit of Picard sheaves, defined globally on the Jacobian of the curve. All such connections are classified; in particular they are all flat. Krichever's algebro-geometric solutions of the KP equations are recovered upon trivializing the resulting \tdD-modules over the complement of the Θ divisor.

Journal

Acta Applicandae MathematicaeSpringer Journals

Published: Jul 1, 2004

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