Full paper in PDF:
$% E. Arrondo, Subcanonicity of codimension two subvarieties, Rev. Mat. Complut. 18 (2005), no. 1, 69–80.%$

Subcanonicity of Codimension Two Subvarieties

Enrique ARRONDO
Departamento de Álgebra
Facultad de Ciencias Matemáticas
Universidad Complutense de Madrid
28040 Madrid Spain

Received: February 5, 2004
Accepted: June 3, 2004
ABSTRACT

We prove that smooth subvarieties of codimension two in Grassmannians of lines of dimension at least six are rationally numerically subcanonical. We prove the same result for smooth quadrics of dimension at least six under some extra condition. The method is quite easy, and only uses Serre’s construction, Porteous formula, and Hodge index theorem.

Key words: subcanonicity, codimension two, Grassmannians, quadrics.
2000 Mathematics Subject Classification:
14M07.