IJPAM: Volume 39, No. 2 (2007)

$p$-FAT POINTS OF A PROJECTIVE SPACE

E. Ballico
Department of Mathematics
University of Trento
380 50 Povo (Trento) - Via Sommarive, 14, ITALY
e-mail: ballico@science.unitn.it


Abstract.Fix an algebraically closed base field $\mathbb {K}$ such that $p:= \mbox{\rm char}(\mathbb {K})>0$, a $p$-power $q$ and any $P\in {\bf {P}}^n$. Let $[q,n]P$ denote the closed subscheme of ${\bf {P}}^n$ whose ideal is generated by all $L^q$, where $L$ is a homogeneous degree $1$ form vanishing at $P$. Hence $([q,n]P)_{red} = \{P\}$ and $\mbox{\rm length}([q,n]P)
= q^n$. Here we study the postulation of zero-dimensional schemes $Z = \sqcup [q_i,n]P_i$.

Received: June 20, 2007

AMS Subject Classification: 14N05

Key Words and Phrases: fat points, $p$-powers

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 39
Issue: 2