IJPAM: Volume 81, No. 2 (2012)

$\mathbb {P}^3$ WITH $h^1(\mathcal {I}_S(m))>0$ AND $\sharp (S) \sim 4m$

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

Abstract. Fix an integer $m\ge 23$. Here we give the list of all finite sets $S\subset \mathbb {P}^3$ such that $\sharp (S)\le 4m$ and $h^1(\mathcal {I}_S(m))>0$. Fix an integer $\epsilon \ge 0$. We prove that if $m\gg \epsilon$, then there is no finite set $A\subset \mathbb {P}^3$ such that $\sharp (A)\le 4m+\epsilon$, $h^0(\mathcal {I}_A(2))=0$, $h^1(\mathcal {I}_A(m)) >0$ and $h^1(\mathcal {I}_{A'}(m)) =0$ for any $A'\subsetneq A$.

Received: June 22, 2012

AMS Subject Classification: 14N05

Key Words and Phrases: postulation, sets in a projective space, sets in a quadric surface

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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: 2