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

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

2011-09-02

arxiv.org/abs/1109.0476v1

Mathematics

Algebraic Geometry

Scientific paper

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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