Abstract

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.

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Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 1347-1367
Launched on MUSE
1996-12-01
Open Access
No
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