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Very Strange Projective Curves

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Abstract

Let Y ⊂ Pn, n ≥ 3, be an integral non-degenerate very strange projective curve, i.e. assume that the general hyperplane section of Y is not in linearly general position; hence we are in characteristic p. Let π: X → Y be the normalization. Set d≔ deg(Y), g≔ Pa(X) and L≔ π* (Oy(1)). Here we prove that d > 2g−2 and in particular h1(X,L) = 0 and h0(X,L) = d+1−g ≥ (d−1)/2 > n+1.

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  1. Dept. of Mathematics, University of Trento, 38050, Povo (TN), Italy

    E. Ballico

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  1. E. Ballico
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Correspondence to E. Ballico.

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Ballico, E. Very Strange Projective Curves. Results. Math. 39, 195–200 (2001). https://doi.org/10.1007/BF03322685

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