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Harmonic tori and generalised Jacobi varieties

McIntosh, I. (2001) Harmonic tori and generalised Jacobi varieties. Communications in Analysis and Geometry, 9 (2). pp. 423-449. ISSN 1019-8385

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This article shows that every non-isotropic harmonic 2-torus in complex projective space factors through a generalised Jacobi variety related to the spectral curve. Each map is composed of a homomorphism into the variety and a rational map off it. The same ideas allow one to construct (pluri)-harmonic maps of finite type from Euclidean space into Grassmannians and the projective unitary groups. Further, some of these maps will be purely algebraic. For maps into complex projective space the algebraic maps of the plane are always doubly periodic i.e. they yield 2-tori. The classification of all these algebraic maps remains open.

Item Type: Article
Institution: The University of York
Academic Units: The University of York > Mathematics (York)
Depositing User: York RAE Import
Date Deposited: 18 Sep 2009 10:25
Last Modified: 18 Sep 2009 10:25
Status: Published
Publisher: International Press
URI: http://eprints.whiterose.ac.uk/id/eprint/5897

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