Codimension two nonsingular subvarieties of quadrics: Scrolls and classification in degree \(d\leq 10\). (English) Zbl 0927.14027

de Cataldo, Mark Andrea A.

J. Math. Soc. Japan 50, No. 4, 879-902 (1998).

Let \(X\) be a codimension two nonsingular subvariety of a nonsingular quadric \({\mathcal Q}^{n}\) of dimension \(n\geq 5\). We classify such subvarieties when they are scrolls. We also classify them when the degree \(d\leq 10\). Both results were known when \(n=4\).

Reviewer: M.A.A.de Cataldo (Bonn)

MSC:

14R05	Classification of affine varieties
14M07	Low codimension problems in algebraic geometry
14J40	\(n\)-folds (\(n>4\))
14M06	Linkage

Keywords:

liaison; low codimension; low degree; quadric; scroll; vector bundle