Please use this identifier to cite or link to this item: http://repositorio.unicamp.br/jspui/handle/REPOSIP/87000
Type: Artigo
Title: Trihyperkähler reduction and instanton bundles on ℂℙ3
Author: Jardim, Marcos
Verbitsky, Misha
Abstract: A trisymplectic structure on a complex 2n-manifold is a three-dimensional space Ω of closed holomorphic forms such that any element of Ω has constant rank 2n, n or zero, and degenerate forms in Ω 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 hyperkähler manifold, and define a trisymplectic reduction of a trisymplectic manifold, which is a complexified form of a hyperkähler reduction. We prove that the trisymplectic reduction in the space of regular rational curves on the twistor space of a hyperkähler manifold M is compatible with the hyperkähler 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.
A trisymplectic structure on a complex 2n-manifold is a three-dimensional space Ω of closed holomorphic forms such that any element of Ω has constant rank 2n, n or zero, and degenerate forms in Ω 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 hyperkähler manifold, and define a trisymplectic reduction of a trisymplectic manifold, which is a complexified form of a hyperkähler reduction. We prove that the trisymplectic reduction in the space of regular rational curves on the twistor space of a hyperkähler manifold M is compatible with the hyperkähler 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.
Subject: Fibrados vetoriais
Instantons
Variedades kahlerianas
Country: Reino Unido
Editor: Cambridge University Press
Citation: Compositio Mathematica. Cambridge University Press, v. 150, n. 11, p. 1836 - 1868, 2014.
Rights: fechado
Identifier DOI: 10.1112/S0010437X14007477
Address: https://www.cambridge.org/core/journals/compositio-mathematica/article/trihyperkahler-reduction-and-instanton-bundles-on-mathbbcmathbbp3/3C098F84AC062E92F866D52CC960523D
Date Issue: 2014
Appears in Collections:IMECC - Artigos e Outros Documentos

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