Trihyperkahler reduction and instanton bundles on CP3

Autor(es)

Jardim, Marcos ^[1] ; Verbitsky, Misha ^{[2, 3]}

Afiliação do(s) autor(es)

^[1] IMECC UNICAMP, Dept Matemat, BR-13083859 Campinas, SP - Brazil

^[2] NRU HSE, Lab Algebra Geometry, Fac Math, Moscow - Russia

^[3] Univ Tokyo, Inst Phys & Math Universe, Kashiwa, Chiba 2778583 - Japan

• Tipo de documento: Artigo Científico
• Fonte: COMPOSITIO MATHEMATICA; v. 150, n. 11, p. 1836-1868, NOV 2014.
• Citações Web of Science: 13

Resumo

A trisymplectic structure on a complex 2n-manifold is a three-dimensional space Q of closed holomorphic forms such that any element of Q has constant rank 2n, n or zero, and degenerate forms in Q belong to a non-degenerate quadric hypersurface. We show that a trisymplectic manifold is equipped with a holomorphic 3-web and the Chern connection of this 3-web is holomorphic, torsion-free, and preserves the three symplectic forms. We construct a trisymplectic structure on the moduli of regular rational curves in the twistor space of a hyperkahler manifold, and define a trisymplectic reduction of a trisymplectic manifold, which is a complexified form of a hyperkahler reduction. We prove that the trisymplectic reduction in the space of regular rational curves on the twistor space of a hyperkahler manifold M is compatible with the hyperkahler reduction on M. As an application of these geometric ideas, we consider the ADHM construction of instantons and show that the moduli space of rank r, charge c framed instanton bundles on CP3 is a smooth trisymplectic manifold of complex dimension 4rc. In particular, it follows that the moduli space of rank two, charge c instanton bundles on CP3 is a smooth complex manifold dimension 8c - 3, thus settling part of a 30-year-old conjecture. (AU)

• Processo FAPESP: 11/01071-3 - Feixes em variedades algébricas e representações de quivers
• Beneficiário: Marcos Benevenuto Jardim
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• Processo FAPESP: 09/12576-9 - A geometria de estruturas hyperkähler
• Beneficiário: Marcos Benevenuto Jardim
• Modalidade de apoio: Auxílio à Pesquisa - Pesquisador Visitante - Internacional