IJPAM: Volume 40, No. 4 (2007)

ALGEBRAIC PROPERTIES OF GRIDS OF FAT LINES

M. Guida$^1$, F. Orecchia$^2$
$^{1 2}$Department of Mathematics and Applications ``R. Caccioppoli"
University of Naples ``Federico II''
Via Cintia, Naples, 80126, ITALY
$^1$e-mail: maguida@unina.it
$^2$e-mail: orecchia@unina.it


Abstract.In this paper we consider the generators of the ideal $I$ defining a grid $X$ of fat lines in the projective space $\mathbb{P}^n$. We compute a minimal set of generators in the homogeneous and quasi-homogeneous cases in $\mathbb{P}^3$. We show also that in these cases the homogeneous coordinate ring of $X$ is always Cohen-Macaulay.

Received: September 14, 2007

AMS Subject Classification: 14M05, 14H50, 14N05

Key Words and Phrases: grids, fat lines, generators, Cohen-Macaulay rings

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 40
Issue: 4