IJPAM: Volume 98, No. 3 (2015)

ZERO-DIMENSIONAL SCHEMES CONTAINED
BETWEEN TWO CONSECUTIVE MULTIPLE POINTS

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


Abstract. Fix an integral projective variety, $P\in X_{reg}$, $m>0$, $L\in \mbox{Pic}(X)$. Let $W\subseteq H^0(X,L)$ be a linear subspace. Set $b:= \dim (W(-mP))$ and $a:= \dim (W(-(m+1)P))$. Fix an integer $z$ such that $0 \le z \le b-a$. We prove the existence of a zero-dimensional scheme $Z\subset X$ such that $mP \subseteq Z\subseteq (m+1)P$, $\deg (Z) = \deg (mP) +z$ and $\dim (W(-Z)) = b-z$.

Received: September 19, 2014

AMS Subject Classification: 14N05

Key Words and Phrases: fat point, zero-dimensional scheme, multiple point

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DOI: 10.12732/ijpam.v98i3.7 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2015
Volume: 98
Issue: 3
Pages: 351 -


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