Geodesic
Zariski Hyperplane Section Theorem for Grassmannian Varieties
Canadian journal of mathematics, Tome 55 (2003) no. 1, pp. 157-180

Voir la notice de l'article provenant de la source Cambridge University Press

Let $\phi :\,X\,\to \,M$ be a morphism from a smooth irreducible complex quasi-projective variety $X$ to a Grassmannian variety $M$ such that the image is of dimension ≥ 2. Let $D$ be a reduced hypersurface in $M$ , and $\gamma $ a general linear automorphism of $M$ . We show that, under a certain differential-geometric condition on $\phi (X)$ and $D$ , the fundamental group ${{\text{ }\!\!\pi\!\!\text{ }}_{1}}\left( {{\left( \gamma \,o\,\phi\right)}^{-1}}\,\left( M\,\backslash \,D \right) \right)$ is isomorphic to a central extension of ${{\pi }_{1}}\left( M\,\backslash \,D \right)\,\,\times \,{{\pi }_{1}}\left( X \right)$ by the cokernel of ${{\pi }_{2}}\left( \phi\right)\,:\,{{\pi }_{2}}\left( X \right)\,\to {{\pi }_{2}}\left( M \right)$ .
DOI : 10.4153/CJM-2003-007-9
Mots-clés : 14F35, 14M15 
Shimada, Ichiro. Zariski Hyperplane Section Theorem for Grassmannian Varieties. Canadian journal of mathematics, Tome 55 (2003) no. 1, pp. 157-180. doi: 10.4153/CJM-2003-007-9
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