Geometry of hyperkähler structures

• Grant number: 09/12576-9
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Start date: November 15, 2009
• End date: August 16, 2010
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Marcos Benevenuto Jardim
• Grantee: Marcos Benevenuto Jardim
• Visiting researcher: Misha Verbitsky
• Visiting researcher institution: University of Tokyo, Japan
• Host 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

Abstract

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)

JARDIM, MARCOS; VERBITSKY, MISHA. Trihyperkahler reduction and instanton bundles on CP3. COMPOSITIO MATHEMATICA, v. 150, n. 11, p. 1836-1868, NOV 2014. (11/01071-3, 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, MAY 2015. (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, JUL 10 2011. (05/04558-0, 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, OCT 2018. (09/12576-9, 14/14743-8)