Multigraded Hilbert functions and toric complete intersection codes

ŞAHİN M., Soprunov I.

JOURNAL OF ALGEBRA, vol.459, pp.446-467, 2016 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 459
  • Publication Date: 2016
  • Doi Number: 10.1016/j.jalgebra.2016.04.013
  • Journal Name: JOURNAL OF ALGEBRA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.446-467
  • Hacettepe University Affiliated: Yes

Abstract

Let X be a complete n-dimensional simplicial toric variety with homogeneous coordinate ring S. We study the multi graded Hilbert function H-Y of reduced 0-dimensional sub schemes Y in X. We provide explicit formulas and prove non-decreasing and stabilization properties of H-Y when Y is a 0-dimensional complete intersection in X. We apply our results to computing the dimension of some evaluation codes on 0-dimensional complete intersection in simplicial toric varieties. (C) 2016 Elsevier Inc. All rights reserved.