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Gibbons-Hermsen varieties and noncommutative geometry

Grant number: 11/09782-6
Support Opportunities:Scholarships in Brazil - Post-Doctorate
Effective date (Start): September 01, 2011
Effective date (End): August 31, 2014
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Geometry and Topology
Principal Investigator:Igor Mencattini
Grantee:Alberto Tacchella
Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil


The aim of this project is a thorough investigation of the geometry of the phase space of the Gibbons-Hermsen integrable system. This is a generalization of the rational Calogero-Moser system in which the point particles are endowed with some additional degrees of freedom. In this research project we propose to extend to the Gibbons-Hermsen system the well-known relationship between the Calogero-Moser phase space, the Hilbert scheme of points in the complex plane and the space of equivalence classes of projective modules of rank 1 in the first Weyl algebra.

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Scientific publications
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
MENCATTINI, IGOR; TACCHELLA, ALBERTO. A Note on the Automorphism Group of the Bielawski-Pidstrygach Quiver. Symmetry Integrability and Geometry-Methods and Applications, v. 9, . (11/09782-6, 10/19201-8)
TACCHELLA, ALBERTO. An introduction to associative geometry with applications to integrable systems. JOURNAL OF GEOMETRY AND PHYSICS, v. 118, n. SI, p. 202-233, . (11/09782-6)
TACCHELLA, ALBERTO. On a family of quivers related to the Gibbons-Hermsen system. JOURNAL OF GEOMETRY AND PHYSICS, v. 93, p. 11-32, . (11/09782-6)

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