Abstract
The subject of this paper is a Jacobian, introduced by F. Lazzeri (unpublished), associated with every compact oriented Riemannian manifold whose dimension is twice an odd number. We study the Torelli and Schottky problem for Lazzeri's Jacobian of flat tori and we compare Lazzeri's Jacobian of Kähler manifolds with other Jacobians.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
[C]Chern, S. S.,Complex Manifold, Instituto de Fisica e Matematica Universidade de Recife, 1959.
[Gre]Green, M., Infinitesimal methods in Hodge theory, inAlgebraic Cycles and Hodge Theory (Albano, A. and Bardelli, E., eds.), Lecture Notes in Math.1594, pp. 1–92, Spriger-Verlag, Berlin-Heidelberg, 1994.
[G]Griffiths, P., Periods of integrals on algebraic manifolds, I; II,Amer. J. Math. 90 (1968), 568–626; 805–865.
[GH]Griffiths, P. andHarris, J.,Principles of Algebraic Geometry, Wiley, New York, 1978.
[LB]Lange, H., andBirkenhake, C.,Complex Abelian Varieties, Springer-Verlag, Berlin, 1992.
[L1]Lieberman, D. I., Higher Picard varieties,Amer. J. Math. 90 (1968), 1165–1199.
[L2]Lieberman, D. I., Intermediate Jacobians, inAlgebraic Geometry, Oslo, 1970 (Oort, F. ed.), pp. 125–139. Wolters-Nordhoff, Groningen, 1972.
[M]Mumford, D.,Abelian Varieties, Tata Institute of Fundamental Research, Bombay; Oxford Univ. Press, London, 1974.
[SP]Séminaire Palaiseau,Première classe de Chern et courbure de Ricci: preuve de la conjecture de Calabi, Astérisque,58, Soc. Math. France, Paris, 1978.
[S]Spanier, E.,Algebraic Topology, McGraw-Hill, New York-Toronto-London, 1966.
[W]Weil, A.,Introduction à l'étude des variétés kählériennes, Hermann, Paris, 1958.
[Wel]Wells, R.,Differential Analysis on Complex Manifolds, Springer-Verlag, Berlin-New York, 1980.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Rubei, E. Lazzeri's Jacobian of oriented compact Riemannian manifolds. Ark. Mat. 38, 381–397 (2000). https://doi.org/10.1007/BF02384326
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02384326