We study the geometrical meaning of the Faà di Bruno polynomials in the context of KP theory. They provide a basis in a subspace W of the universal Grassmannian associated to the KP hierarchy. When W comes from geometrical data via the Krichever map, the Faà di Bruno recursion relation turns out to be the cocycle condition for (the Welters hypercohomology group describing) the deformations of the dynamical line bundle on the spectral curve together with the meromorphic sections which give rise to the Krichever map. Starting from this, one sees that the whole KP hierarchy has a similar cohomological meaning.

Krichever Maps, Faà  di Bruno Polynomials, and Cohomology in KP Theory / Falqui, Gregorio; Reina, Cesare; Zampa, A.. - In: LETTERS IN MATHEMATICAL PHYSICS. - ISSN 0377-9017. - 42:4(1997), pp. 349-361. [10.1023/A:1007323118991]

Krichever Maps, Faà  di Bruno Polynomials, and Cohomology in KP Theory

Falqui, Gregorio;Reina, Cesare;
1997-01-01

Abstract

We study the geometrical meaning of the Faà di Bruno polynomials in the context of KP theory. They provide a basis in a subspace W of the universal Grassmannian associated to the KP hierarchy. When W comes from geometrical data via the Krichever map, the Faà di Bruno recursion relation turns out to be the cocycle condition for (the Welters hypercohomology group describing) the deformations of the dynamical line bundle on the spectral curve together with the meromorphic sections which give rise to the Krichever map. Starting from this, one sees that the whole KP hierarchy has a similar cohomological meaning.
1997
42
4
349
361
https://arxiv.org/abs/solv-int/9704010
Falqui, Gregorio; Reina, Cesare; Zampa, A.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/59282
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