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Geometry of hyperkähler structures

Grant number: 09/12576-9
Support type:Research Grants - Visiting Researcher Grant - International
Duration: November 15, 2009 - August 16, 2010
Field of knowledge:Physical Sciences and Mathematics - Mathematics
Principal Investigator:Marcos Benevenuto Jardim
Grantee:Marcos Benevenuto Jardim
Visiting researcher: Misha Verbitsky
Visiting researcher institution: University of Tokyo, Japan
Home Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
Associated research grant:05/04558-0 - Symmetries in geometry, topology and mathematical physics, AP.TEM


We propose to investigate concrete geometric and topological properties related to hyperkähler manifolds, existence of differentiable structures, and of relevant deformations. In particular, we also propose to investigate what geometric structures (hypercomplex, quaternionic kahler, hyperkähler, etc) arise in nonsingular locus of the moduli spaces of instanton bundles over complex projective spaces of dimension n. For n=2, such space is known to cary a hyperkähler metric; the case n=3 is open, and already of great interest. (AU)

Scientific publications (4)
(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)
HENNI, ABDELMOUBINE A.; JARDIM, MARCOS. Commuting matrices and the Hilbert scheme of points on affine spaces. ADVANCES IN GEOMETRY, v. 18, n. 4, p. 467-482, OCT 2018. Web of Science Citations: 0.
HENNI, ABDELMOUBINE AMAR; JARDIM, MARCOS; MARTINS, RENATO VIDAL. ADHM CONSTRUCTION OF PERVERSE INSTANTON SHEAVES. Glasgow Mathematical Journal, v. 57, n. 2, p. 285-321, MAY 2015. Web of Science Citations: 2.
JARDIM, MARCOS; VERBITSKY, MISHA. Trihyperkahler reduction and instanton bundles on CP3. COMPOSITIO MATHEMATICA, v. 150, n. 11, p. 1836-1868, NOV 2014. Web of Science Citations: 14.
JARDIM, MARCOS; VERBITSKY, MISHA. Moduli spaces of framed instanton bundles on CP3 and twistor sections of moduli spaces of instantons on C-2. ADVANCES IN MATHEMATICS, v. 227, n. 4, p. 1526-1538, JUL 10 2011. Web of Science Citations: 4.

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