IJPAM: Volume 81, No. 3 (2012)

Superficial defective subschemes of $\mathbb {P}^3$

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


Abstract. We prove that the zero-dimensional superficial schemes $Z\subset \mathbb {P}^3$ such that $\deg (Z)\le 3m$ and $h^1(\mathcal {I}_Z(m))=0$ are only the expected ones (`` superficial '' means that the Zariski tangent spaces have dimension $\le 2$).

Received: July 18, 2012

AMS Subject Classification: 14N05

Key Words and Phrases: postulation, zero-dimensional scheme, 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: 3