Connections on the total Picard sheaf and the KP hierarchy
type: Item
instance of: scholarly article
title: Connections on the total Picard sheaf and the KP hierarchy
zbMATH Open document ID: 0848.58032
DOI: 10.1007/BF01064170
published in: Acta Applicandae Mathematicae
publication date: 1996-10-27T00:00:00Z
review text: The paper is inspired by \textit{D. Mumford} [Proc. Int. Symp. Alg. Geom. Kyoto 1977, 115-153 (1977; Zbl 0423.14007)] and analysis of the Krichever approach to KP equations [see also \textit{G. Segal} and \textit{G. Wilson}, Publ. Math., Inst. Hautes Étud. Sci. 65, 5-65 (1985; Zbl 0592.35112)]. The construction relies on certain special flat connections \(\nabla\) on the total Picard sheaf \(\mathcal E\) (a direct limit of Poincaré sheaves of a curve) defined on the Jacobian of the curve. To get the KP hierarchy, \(\mathcal E\) is embedded in a formal completion \(\widehat {\mathcal E}\) equipped with the sheaf of pseudodifferential operators. Then \(\mathcal E\) and \(\widehat {\mathcal E}\) naturally trivialize by a connection which is not \(\nabla\), and the difference yields the sought hierarchy.
Mathematics Subject Classification ID: 37J35
Mathematics Subject Classification ID: 37K10
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 14H99
zbMATH DE Number: 854832
zbMATH Keywords: connections
zbMATH Keywords: Picard sheaf
zbMATH Keywords: Poincaré sheaves
zbMATH Keywords: KP hierarchy
author: Mitchell J. Rothstein
reviewed by: Jan Chrastina
MaRDI profile type: Publication
cites work: Commutative ordinary differential operators. II.—The identity P n = Q m
cites work: Q4134307
cites work: Integration of nonlinear equations by the methods of algebraic geometry
cites work: Q3856866
cites work: Q5628266
cites work: Loop groups and equations of KdV type
description: scientific article; zbMATH DE number 854832