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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
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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
Opis fizyczny
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)
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-012-0062-2
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