IJPAM: Volume 81, No. 1 (2012)

DEFECTIVE CURVILINEAR SUBSCHEMES
IN PROJECTIVE SPACES

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


Abstract. Let $Z\subset \mathbb {P}^r$, $r\ge 3$, be a curvilinear zero-dimensional scheme such that $\deg (Z)\le 4m+r-5$, $Z$ spans $\mathbb {P}^r$, $\deg (Z\cap M)<3m$ for each $3$-dimensional linear subspace $M\subseteq \mathbb {P}^r$ and $h^1(\mathcal {I}_Z(m))>0$. Then either there is a line $D$ with $\deg (D\cap Z)\ge m+2$ or there is a conic $T$ with $\deg (T\cap Z)\ge 2m+2$.

Received: July 1, 2012

AMS Subject Classification: 14N05

Key Words and Phrases: postulation of finite sets, Hilbert function

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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: 81
Issue: 1