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.
@article{urn:eudml:doc:44544, title = {Subcanonicity of codimension two subvarieties.}, journal = {Revista Matem\'atica de la Universidad Complutense de Madrid}, volume = {18}, year = {2005}, pages = {69-80}, zbl = {1078.14070}, mrnumber = {MR2135532}, language = {en}, url = {http://dml.mathdoc.fr/item/urn:eudml:doc:44544} }
Arrondo, Enrique. Subcanonicity of codimension two subvarieties.. Revista Matemática de la Universidad Complutense de Madrid, Tome 18 (2005) pp. 69-80. http://gdmltest.u-ga.fr/item/urn:eudml:doc:44544/