CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  PublicationsjournalsCJM
Abstract view

Decompositions of the Hilbert Function of a Set of Points in $\P^n$

  Published:2001-10-01
 Printed: Oct 2001
  • Anthony V. Geramita
  • Tadahito Harima
  • Yong Su Shin
Features coming soon:
Citations   (via CrossRef) Tools: Search Google Scholar:
Format:   HTML   LaTeX   MathJax   PDF   PostScript  

Abstract

Let $\H$ be the Hilbert function of some set of distinct points in $\P^n$ and let $\alpha = \alpha (\H)$ be the least degree of a hypersurface of $\P^n$ containing these points. Write $\alpha = d_s + d_{s-1} + \cdots + d_1$ (where $d_i > 0$). We canonically decompose $\H$ into $s$ other Hilbert functions $\H \leftrightarrow (\H_s^\prime, \dots, \H_1^\prime)$ and show how to find sets of distinct points $\Y_s, \dots, \Y_1$, lying on reduced hypersurfaces of degrees $d_s, \dots, d_1$ (respectively) such that the Hilbert function of $\Y_i$ is $\H_i^\prime$ and the Hilbert function of $\Y = \bigcup_{i=1}^s \Y_i$ is $\H$. Some extremal properties of this canonical decomposition are also explored.
MSC Classifications: 13D40, 14M10 show english descriptions Hilbert-Samuel and Hilbert-Kunz functions; Poincare series
Complete intersections [See also 13C40]
13D40 - Hilbert-Samuel and Hilbert-Kunz functions; Poincare series
14M10 - Complete intersections [See also 13C40]
 

© Canadian Mathematical Society, 2014 : http://www.cms.math.ca/