IJPAM: Volume 78, No. 2 (2012)

SUBSCHEMES OF $\mathbb {P}^r$

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

Abstract. Fix a zero-dimensional scheme $E\subset \mathbb {P}^r$ and an integer $t>0$ such that $h^1(\mathcal {I}_E(t)) =0$. Here we study the set of all $P\in \mathbb {P}^r\setminus E_{red}$ such that $h^0(\mathcal {I}_{E\cup \{P\}}(t)) = h^0(\mathcal {I}_E(t))$ and $h^0(\mathcal {I}_{E'\cup \{P\}}(t)) < h^0(\mathcal {I}_{E'}(t))$ for all $E'\subsetneq E$.

Received: January 16, 2012

AMS Subject Classification: 14N05

Key Words and Phrases: zero-dimensional scheme, Gorenstein zero-dimensional scheme, base locus

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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: 2