Ir al contenido

Documat


Moduli spaces of framed instanton bundles on CP3 and twistor sections of moduli spaces of instantons on C2

  • Autores: Marcos Jardim Árbol académico, Misha Verbitsky
  • Localización: Advances in mathematics, ISSN 0001-8708, Vol. 227, Nº 4, 2011, págs. 1526-1538
  • Idioma: inglés
  • DOI: 10.1016/j.aim.2011.03.012
  • Texto completo no disponible (Saber más ...)
  • Resumen
    • We show that the moduli space M of framed instanton bundles on CP3 is isomorphic (as a complex manifold) to a subvariety in the moduli of rational curves of the twistor space of the moduli space of framed instantons on R-4. We then use this characterization to prove that M is equipped with a torsion-free affine connection with holonomy in Sp(2n, C).

  • Referencias bibliográficas
    • M.F. Atiyah, Complex analytic connections in fibre bundles, Trans. Amer. Math. Soc. 85 (1957) 181–207.
    • S.S. Chern, Eine Invariantentheorie der Dreigewebe aus r-dimensionalen Mannigfaltigkeiten im R2r, Abhandl. Math. Semin. Univ. Hamburg, 1936.
    • I. Coand˘a, A.S. Tikhomirov, G. Trautmann, Irreducibility and smoothness of the moduli space of mathematical 5-instantons over P3, Internat....
    • S. Donaldson, Instantons and geometric invariant theory, Comm. Math. Phys. 93 (1984) 453–460.
    • B. Feix, Hyperkähler metrics on cotangent bundles, Ph.D. thesis, Oxford, 1999, 78 pp.
    • B. Feix, Hyperkähler metrics on cotangent bundles, J. Reine Angew. Math. 532 (2001) 33–46.
    • I.B. Frenkel, M. Jardim, Complex ADHM equations, and sheaves on P3, J. Algebra 319 (2008) 2913–2937.
    • H. Grauert, G. Mülich, Vectorbundel von Rang 2 uber dem n-dimensionalen komplex projective Raum, Manuscripta Math. 16 (1975) 75–100.
    • M. Hauzer, A. Langer, Moduli spaces of framed perverse instantons on P3, Glasg. Math. J. 53 (2010) 51–96.
    • M. Jardim, Instanton sheaves on complex projective spaces, Collect. Math. 57 (2006) 69–97.
    • M. Jardim, Atiyah–Drinfeld–Hitchin–Manin construction of framed instanton sheaves, C. R. Acad. Sci. Paris Ser. I 346 (2008) 427–430.
    • D. Kaledin, Hyperkähler structures on total spaces of holomorphic cotangent bundles, in: D. Kaledin, M. Verbitsky (Eds.), Hyperkähler Manifolds,...
    • D. Kaledin, M. Verbitsky, Non-Hermitian Yang–Mills connections, Selecta Math. (N.S.) 4 (1998) 279–320.
    • M. Maruyama, The Theorem of Grauert–Mülich–Spindler, Math. Ann. 255 (1981) 317–333.
    • P.T. Nagy, Invariant tensorfields and the canonical connection of a 3-web, Aequationes Math. 35 (1988) 31–44.
    • H. Nakajima, Lectures on Hilbert Schemes of Points on Surfaces, American Mathematical Society, Providence, 1999.
    • T. Nitta, Vector bundles over quaternionic Kähler manifolds, Tohoku Math. J. 40 (1988) 425–440.
    • S. Salamon, Quaternionic Kähler manifolds, Invent. Math. 67 (1982) 143–171.
    • A.A. Tikhomirov, The main component of the moduli space of mathematical instanton vector bundles on P3, J. Math. Sci. 86 (1997) 3004–3087.
    • M. Verbitsky, Hyperholomorphic bundles over a hyperkähler manifold, J. Algebraic Geom. 5 (1996) 633–669.
    • M. Verbitsky, Hypercomplex varieties, Comm. Anal. Geom. 7 (1999) 355–396.

Fundación Dialnet

Mi Documat

Opciones de artículo

Opciones de compartir

Opciones de entorno