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arXiv · 1109.0476

Embeddings of general curves in projective spaces: the range of the quadrics

Edoardo Ballico
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Abstract

Let $C \subset \mathbb {P}^r$ a general embedding of prescribed degree of a general smooth curve with prescribed genus. Here we prove that either $h^0(\mathbb {P}^r,\mathcal {I}_C(2)) =0$ or $h^1(\mathbb {P}^r,\mathcal {I}_C(2)) =0$ (a problem called the Maximal Rank Conjecture in the range of quadrics).

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Edoardo Ballico. 2011-09-02. Embeddings of general curves in projective spaces: the range of the quadrics. https://arxiv.org/abs/1109.0476

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