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On majore la dimension de l’ensemble des hypersurfaces de dont l’intersection avec une variété projective intègre fixée n’est pas intègre. Les majorations obtenues sont optimales. Comme application, on construit, quand c’est possible, des hypersurfaces dont les intersections avec toutes les variétés d’une famille de variétés projectives intègres sont intègres. Le degré des hypersurfaces construites est explicite.
For low order jets, it is known how to construct meromorphic frames on the space of the so-called vertical -jets of the universal hypersurfaceparametrizing all projective hypersurfaces of degree . In 2004, for , Siu announced that there exist two constants and such that the twisted tangent bundleis generated at every point by its global sections. In the present article, we establish this property outside a certain exceptional algebraic subset defined by the vanishing of certain Wronskians,...
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