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Geometry of hyperkähler structures


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)

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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)
JARDIM, MARCOS; VERBITSKY, MISHA. Trihyperkahler reduction and instanton bundles on CP3. COMPOSITIO MATHEMATICA, v. 150, n. 11, p. 1836-1868, . (11/01071-3, 09/12576-9)
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, . (05/04558-0, 09/12576-9)
HENNI, ABDELMOUBINE AMAR; JARDIM, MARCOS; MARTINS, RENATO VIDAL. ADHM CONSTRUCTION OF PERVERSE INSTANTON SHEAVES. Glasgow Mathematical Journal, v. 57, n. 2, p. 285-321, . (11/01071-3, 09/12576-9)
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, . (09/12576-9, 14/14743-8)

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