IJPAM: Volume 77, No. 3 (2012)

THE MAXIMAL RANK CONJECTURE FOR LINEARLY
NORMAL CURVES $C\subset \mathbb {P}^r$ with $h^1(C,\mathcal {O}_C(1))=1$

E. Ballico
Department of Mathematics
University of Trento
38 123 Povo (Trento) - Via Sommarive, 14, ITALY
e-mail: ballico@science.unitn.it


Abstract. Let $C\subset \mathbb {P}^r$ be a general linearly normal curve with prescribed genus and $h^1(C,\mathcal {O}_C(1))=1$. Here we prove that $C$ has maximal rank, i.e. that for all integers $t$ the restriction map $H^0(\mathbb {P}^r,\mathcal {O}_{\mathbb {P}^r}(t)) \to H^0(C,\mathcal {O}_C(t))$ is either injective or surjective.

Received: August 27, 2011

AMS Subject Classification: 14H50

Key Words and Phrases: maximal rank, curves with general moduli, postulation

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 77
Issue: 3