IJPAM: Volume 78, No. 8 (2012)

WITH MAXIMAL RANK IN $\mathbb {P}^r$

E. Ballico
Department of Mathematics
University of Trento
38 123 Povo (Trento) - Via Sommarive, 14, ITALY

Abstract. Fix integers $r, g$ such that $r\ge 4$ and $g\ge r+1$. Let $C\subset \mathbb {P}^r$ be a general smooth curve with genus $g$, degree $g+r$ and $h^1(C,\mathcal {O}_C(1))=1$ (such a curve is not linearly normal). In this paper we prove that $C$ has maximal rank, i.e. $h^0(\mathcal {I}_C(t))\cdot h^1(\mathcal {I}_C(t)) =0$ for all $t\in \mathbb {N}$.

Received: March 28, 2012

AMS Subject Classification: 14H51, 4N05

Key Words and Phrases: postulation, curve with maximal rank, non-linearly normal embedding

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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: 78
Issue: 8