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EQUATIONS OF THE MODULI OF HIGGS PAIRS AND INFINITE GRASSMANNIAN

Departamento de Matemáticas and Instituto, Universitario de Física Fundamental y Matemáticas (IUFFYM), Universidad de Salamanca, Plaza de la Merced 1-4, 37008 Salamanca, Spain

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J. M. MUÑOZ PORRAS

Departamento de Matemáticas and Instituto, Universitario de Física Fundamental y Matemáticas (IUFFYM), Universidad de Salamanca, Plaza de la Merced 1-4, 37008 Salamanca, Spain

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F. J. PLAZA MARTÍN

Departamento de Matemáticas and Instituto, Universitario de Física Fundamental y Matemáticas (IUFFYM), Universidad de Salamanca, Plaza de la Merced 1-4, 37008 Salamanca, Spain

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https://doi.org/10.1142/S0129167X09005637Cited by:2 (Source: Crossref)

Abstract

In this paper the moduli space of Higgs pairs over a fixed smooth projective curve with extra formal data is defined and is endowed with a scheme structure. We introduce a relative version of the Krichever map using a fibration of Sato Grassmannians and show that this map is injective. This, together with the characterization of the points of the image of the Krichever map, allows us to prove that this moduli space is a closed subscheme of the product of the moduli of vector bundles (with formal extra data) and a formal anologue of the Hitchin base. This characterization also provides us with a method for explicitly computing KP-type equations that describe the moduli space of Higgs pairs. Finally, for the case where the spectral cover is totally ramified at a fixed point of the curve, these equations are given in terms of the characteristic coefficients of the Higgs field.

Keywords:

AMSC: 14H60, 37K10, 14H10, 14H70, 58B99

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