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On cohomology of the square of an ideal sheaf. (English) Zbl 0892.14022
The main result in this paper is to give some necessary conditions on \(C\subset \mathbb{P}^{g-1}\), the canonical embedding of a non-hyperelliptic curve, which imply that \(C\) is a hyperplane section of a surface distinct of a cone. One of these conditions is the vanishing of the cohomology groups \(H^1(\mathbb{P}^{g-1}, I^2_C(k))\), for \(k\geq 3\). The paper contains several results and a conjecture on this vanishing property.
Reviewer: A.Dimca (Bordeaux)

MSC:
14M10 Complete intersections
14F17 Vanishing theorems in algebraic geometry
14E25 Embeddings in algebraic geometry
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