IJPAM: Volume 74, No. 3 (2012)

EMBEDDINGS OF GENERAL CURVES IN
PROJECTIVE SPACES:
PARTS OF THE RANGE OF THE CUBICS

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


Abstract. Here we prove the existence of linearly normal smooth curves $C\subset \mathbb {P}^r$, $r\ge 5$, with maximal rank, $h^1(X,\mathcal {O}_C(1)) \le r/2$, any genus at most of order $r^3/12$ and general moduli. In this range of degrees and genera we prove the surjectivity of the restriction map $H^0(\mathbb {P}^r,\mathcal {O}_{\mathbb {P}^r}(3)) \to H^0(C,\mathcal {O}_C(3))$.

Received: September 5, 2011

AMS Subject Classification: 14H50, 14H51

Key Words and Phrases: postulation, curve with general moduli, maximal rank conjecture, cubic hypersurfaces

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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: 74
Issue: 3