On the Picard number of divisors in Fano manifolds
نویسنده
چکیده
Let X be a complex Fano manifold of arbitrary dimension, and consider a prime divisor D ⊂ X. We denote by N1(D,X) the linear subspace of N1(X) spanned by numerical classes of curves contained in D, i.e. N1(D,X) = i∗(N1(D)) where i∗ : N1(D) → N1(X) is the push-forward of one-cycles induced by the inclusion i : D →֒ X. The codimension of N1(D,X) in N1(X) equals the dimension of the kernel of the restriction N (X) → N (D). If X is a Del Pezzo surface, then codimN1(D,X) = ρS−1 ≤ 8. Our main result is that the same holds in general.
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تاریخ انتشار 2009