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2012 | 10 | 4 | 1232-1245

Tytuł artykułu

Moduli of symplectic instanton vector bundles of higher rank on projective space ℙ3

Treść / Zawartość

Języki publikacji

EN

Abstrakty

EN
Symplectic instanton vector bundles on the projective space ℙ3 constitute a natural generalization of mathematical instantons of rank-2. We study the moduli space I n;r of rank-2r symplectic instanton vector bundles on ℙ3 with r ≥ 2 and second Chern class n ≥ r, n ≡ r (mod 2). We introduce the notion of tame symplectic instantons by excluding a kind of pathological monads and show that the locus I n;r* of tame symplectic instantons is irreducible and has the expected dimension, equal to 4n(r + 1) −r(2r + 1).

Słowa kluczowe

Wydawca

Czasopismo

Rocznik

Tom

10

Numer

4

Strony

1232-1245

Daty

wydano
2012-08-01
online
2012-05-31

Twórcy

Bibliografia

  • [1] Atiyah M.F., Geometry of Yang-Mills Fields, Accademia Nazionle dei Lincei, Scuola Normale Superiore, Pisa, 1979
  • [2] Atiyah M.F., Hitchin N.J., Drinfeld V.G., Manin Yu.I., Construction of instantons, Phys. Lett. A, 1978, 65(3), 185–187 http://dx.doi.org/10.1016/0375-9601(78)90141-X
  • [3] Atiyah M.F., Ward R.S., Instantons and algebraic geometry, Comm. Math. Phys., 1977, 55(2), 117–124 http://dx.doi.org/10.1007/BF01626514
  • [4] Barth W., Lectures on mathematical instanton bundles, In: Gauge Theories: Fundamental Interactions and Rigorous Results, Poiana Brasov, August 25–September 7, 1981, Progr. Phys., 5, Birkhäuser, Boston, 1982, 177–206
  • [5] Barth W., Hulek K., Monads and moduli of vector bundles, Manuscripta Math., 1978, 25(4), 323–347 http://dx.doi.org/10.1007/BF01168047
  • [6] Beilinson A.A., Coherent sheaves on ℙn and problems of linear algebra, Funct. Anal. Appl., 1978, 12(3), 214–216 http://dx.doi.org/10.1007/BF01681436
  • [7] Horrocks G., Vector bundles on the punctured spectrum of a local ring, Proc. London Math. Soc., 1964, 14, 684–713
  • [8] Jardim M., Verbitsky M., Trihyperkähler reduction and instanton bundles on ℂℙ3, preprint available at http://arxiv.org/abs/1103.4431
  • [9] McCarthy P.J., Rational parametrisation of normalised Stiefel manifolds, and explicit non-’t Hooft solutions of the Atiyah-Drinfeld-Hitchin-Manin instanton matrix equations for Sp(n), Lett. Math. Phys., 1981, 5(4), 255–261 http://dx.doi.org/10.1007/BF00401473
  • [10] Tikhomirov A.S., Moduli of mathematical instanton vector bundles with odd c 2 on projective space, Izv. Ross. Akad. Nauk Ser. Mat., 2012, 76(5) (in press, in Russian)
  • [11] Tjurin A.N., On the superposition of mathematical instantons. II, Progr. Math., 36, Birkhäuser, Boston, 1983
  • [12] Tyurin A.N., The structure of the variety of pairs of commuting pencils of symmetric matrices, Izv. Akad. Nauk SSSR Ser. Mat., 1982, 46(2), 409–430 (in Russian)

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bwmeta1.element.doi-10_2478_s11533-012-0062-2