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Gibbons-Hermsen varieties and noncommutative geometry

Grant number: 11/09782-6
Support Opportunities:Scholarships in Brazil - Post-Doctoral
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)
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)
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)
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)

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