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On multiples of divisors associated to Veronese embeddings with defective secant variety

In this note we consider multiples aD, where D is a divisor of the blow-up of P^n along points in general position which appears in the Alexander and Hirschowitz list of Veronese embeddings having defective secant varieties. In particular we show that there is such a D with h^1(X,D) > 0 and h^1(X,2D) = 0.

preprint2010arXivOpen access
Antonio LafaceLuca Ugaglia
math.AG
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Antonio LafaceLuca Ugaglia

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