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Journal Article

Ample Divisors on the Blow up of Pn at Points

E. Ballico
Proceedings of the American Mathematical Society
Vol. 127, No. 9 (Sep., 1999), pp. 2527-2528
Stable URL: http://www.jstor.org/stable/119548
Page Count: 2

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Topics: Smooth curves, Mathematical theorems, Scrolls
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Abstract

Fix integers n, k, d with n ≥ 2, d ≥ 2 and k > 0; if n = 2 assume d ≥ 3. Let P1, ... , Pk be general points of the complex projective space Pn and let π : X → Pn be the blow up of Pn at P1, ... , Pk with exceptional divisors Ei:= π -1(Pi), 1 ≤ i ≤ k. Set H:= π *( O Pn (1)). Here we prove that the divisor L:= dH - ∑1≤ i≤ kEi is ample if and only if Ln > 0, i.e. if and only if dn > k.

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