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On projective degenerations of Veronese spaces

Edoardo Ballico (1996)

Banach Center Publications

Here we give several examples of projective degenerations of subvarieties of t . The more important case considered here is the d-ple Veronese embedding of n ; we will show how to degenerate it to the union of d n n-dimensional linear subspaces of t ; t : = ( n + d ) / ( n ! d ! ) - 1 and the union of scrolls. Other cases considered in this paper are essentially projective bundles over important varieties. The key tool for the degenerations is a general method due to Moishezon. We will give elsewhere several applications to postulation...

On standard norm varieties

Nikita A. Karpenko, Alexander S. Merkurjev (2013)

Annales scientifiques de l'École Normale Supérieure

Let  p be a prime integer and F a field of characteristic 0 . Let  X be thenorm varietyof a symbol in the Galois cohomology group H n + 1 ( F , μ p n ) (for some n 1 ), constructed in the proof of the Bloch-Kato conjecture. The main result of the paper affirms that the function field F ( X ) has the following property: for any equidimensional variety Y , the change of field homomorphism CH ( Y ) CH ( Y F ( X ) ) of Chow groups with coefficients in integers localized at  p is surjective in codimensions < ( dim X ) / ( p - 1 ) . One of the main ingredients of the proof is a computation...

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