-
Théorèmes de connexité pour les produits d'espaces projectifs et les Grassmanniennes
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 118, Number 6, December 1996
- pp. 1347-1367
- 10.1353/ajm.1996.0047
- Article
- Additional Information
- Purchase/rental options available:
We give a numerical condition on the images of two morphisms to a Grassmannian (or a product of projective spaces) that ensures that their fibered product is connected, thereby extending connectedness results of Fulton and Hansen. This result is valid over any algebraically closed field; it yields a condition on the class of an irreducible subvariety of a Grassmannian that implies that it is simply connected. This applies in particular to Fano varieties of certain hypersurfaces in a projective space.