PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo
2003 | 1 | 4 | 661-669
Tytuł artykułu

On representation theory and the cohomology rings of irreducible compact hyperkähler manifolds of complex dimension four

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper, we continue the study of the possible cohomology rings of compact complex four dimensional irreducible hyperkähler manifolds. In particular, we prove that in the case b 2=7, b 3=0 or 8. The latter was achieved by the Beauville construction.
Wydawca
Czasopismo
Rocznik
Tom
1
Numer
4
Strony
661-669
Opis fizyczny
Daty
wydano
2003-12-01
online
2003-12-01
Twórcy
autor
  • The University of California at Riverside
Bibliografia
  • [1] F. Bogomolov: “Kähler manifolds with trivial canonical class”, Izv. Akad. Nauk. SSSR Ser. Mat., Vol. 38, (1974), pp. 11–21.
  • [2] F. Bogomolov: “The decomposition of Kähler manifolds with a trivial canonical class”, Mat. Sb. (N.S.), Vol. 38, (1974), pp. 573–575.
  • [3] F. Bogomolov: “Hamiltonian Kählerian manifolds”, Dolk. Akad. Nauk. SSSR, Vol. 243, (1978), pp. 1101–1104.
  • [4] F. Bogomolov: “On the cohomology ring of a simple hyperkähler manifold (on the results of Verbisky)”, Geom. Funct. Anal., Vol. 6, (1996), pp. 612–618. http://dx.doi.org/10.1007/BF02247113
  • [5] A. Beauville: “Variétés Kähleriennes dont la premirè classe de Chern est nulle”, J. Differential Geometry, Vol. 18, (1983), pp. 755–782.
  • [6] C. Chevalley: The Algebraic Theory of Spinors, Columbia University Press, New York, 1954.
  • [7] D. Guan: “Toward a classification of compact complex homogeneous spaces”, preprint, 1998.
  • [8] Z. Guan: “Toward a classification of almost homogeneous manifolds I-linearization of the singular extremal rays”, International J. Math., Vol. 8, (1997), pp. 999–1014. http://dx.doi.org/10.1142/S0129167X97000470
  • [9] D. Guan: “Examples of compact holomorphic symplectic manifolds which are not Kählerian II”, Invent Math., Vol. 121, (1995), pp. 135–145. http://dx.doi.org/10.1007/BF01884293
  • [10] D. Guan: “Examples of compact holomorphic symplectic manifolds which are not Kählerian III”, Intern. J. of Math., Vol. 6, (1995), pp. 709–718. http://dx.doi.org/10.1142/S0129167X95000298
  • [11] D. Guan: “On Riemann-Roch formula and bounds of the Betti numbers of irreducible compact hyperkähler manifold of complex dimension four”, first version in 1999, a part of paper appeared in Math. Res. Letters, Vol. 8, (2001), pp. 663–669.
  • [12] J. Humphreys: Introduction to Lie Algebras and Representation Theory, GTM 9, Springer-Verlag, New York, 1987.
  • [13] M. Knus, A. Merkurjev, M. Rost, J. Tignol: The Book of Involutions, Colloquium Publications 44, AMS, Providence, Rhode Island, USA, 1998.
  • [14] E. Looijenga and V. Lunts: “A Lie algebra attached to a projective variety”, Invent. Math., Vol. 129, (1997), pp. 361–412. http://dx.doi.org/10.1007/s002220050166
  • [15] K. O'Grady: “Desingularized moduli spaces of sheaves on a K3”, J. Reine Angew. Math., Vol. 512, (1999), pp. 49–117.
  • [16] K. O'Grady: “A new six dimensional irreducible symplectic variety”, preprint, 2000.
  • [17] W. Scharlau: “Quadratic and Hermitian Forms”, Grundlehren der mathematischen Wissenschaften 270, Springer-Verlag, Berlin-Heidelberg-New York-Tokyo, 1985.
  • [18] S. Salamon: “Riemannian Geometry and Holonomy Groups”, Pitman Research Notes in Mathematics, Series 201, 1989.
  • [19] S. Salamon: “On the cohomology of Kähler and hyperkähler manifolds”, Topology, Vol. 35, (1996), pp. 137–155. http://dx.doi.org/10.1016/0040-9383(95)00006-2
  • [20] J. Tits: “Représentations linéaires irréducibles d'un groupe réductif sur un corps quelconque”, J. reine angew. Math., Vol. 247, (1971), pp. 196–220.
  • [21] M. Verbitsky: “Action of the Lie algebra of SO(5) on the cohomology of a hyperkähler manifold”, Functional Anal. appl., Vol. 24, (1991), pp. 229–230. http://dx.doi.org/10.1007/BF01077967
  • [22] M. Verbitsky: “Cohomology of compact hyperkähler manifolds and its applications”, Geom. Funct. Anal., Vol. 6, (1996), pp. 601–611. http://dx.doi.org/10.1007/BF02247112
  • [23] M. Verbitsky and D. Kaledin: Hyperkähler Manifolds, International Press, Somerville, Massachusetts, USA, 1999.
  • [24] S. Yau: “On the Ricci curvature of a compact Kähler manifold and the complex Monge-Ampère equation I”, Comm. Pure Appl. Math., Vol. 31, (1978), pp. 339–411.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_BF02475186
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.