Abstract
Two Picard numbers and two Lefschetz numbers are defined for a real algebraic surface. They are similar to the Picard number and the Lefschetz number of a complex algebraic surface. For these numbers, some estimates and relations in the form of inequalities are proved.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
V. A. Krasnov, “Characteristic classes of vector bundles on a real algebraic manifold,”Izv. Akad. Nauk SSSR Ser. Mat. [Math. USSR-Izv.],55, No. 4, 716–746 (1991).
V. A. Krasnov, “The Brouwer cohomology group of a real algebraic manifold,”Izv. Ross. Akad. Nauk Ser. Mat. [Russian Acad. Sci. Izv. Math.],60, No. 5, 57–88 (1996).
V. M. Kharlamov, “A generalized Petrovskii inequality,”Funktsional. Anal. i Prilozhen. [Functional Anal. Appl.],8, No. 2, 50–56 (1974).
V. A. Krasnov, “Equivariant Grothendieck cohomology of a real algebraic manifold and applications,”Izv. Ross. Akad. Nauk Ser. Mat. [Russian Acad. Sci. Izv. Math.],58, No. 3, 36–52 (1994).
V. A. Krasnov, “Algebraic cycles on a real algebraicGM-manifold and applications,”Izv. Ross. Akad. Nauk Ser. Mat. [Russian Acad. Sci. Izv. Math.],57, No. 4, 153–173 (1993).
V. A. Krasnov, “Harnack-Thom inequalities for mappings of real algebraic manifolds,”Izv. Akad. Nauk SSSR Ser. Mat. [Math. USSR-Izv.],47, No. 2, 268–297 (1983).
Author information
Authors and Affiliations
Additional information
Translated fromMatematicheskie Zametki, Vol. 63, No. 6, pp. 847–852, June, 1998.
Rights and permissions
About this article
Cite this article
Krasnov, V.A. Picard and Lefschetz numbers of real algebraic surfaces. Math Notes 63, 747–751 (1998). https://doi.org/10.1007/BF02312767
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02312767