Multigraded Hilbert function and toric complete intersection codes

Abstract

Let $X$ be a complete $n$-dimensional simplicial toric variety with homogeneous coordinate ring $S$. We study the multigraded Hilbert function $H_Y$ of reduced $0$-dimensional subschemes $Y$ 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.

22 pages, comments welcome, presented at ICM 2014, Seoul, KOREA

References in corpus (1)

• Toric complete intersection codes

Cited by in corpus (2)

• Toric Codes and Lattice Ideals
• On dual toric complete intersection codes