Reverse Lexicographic Gröbner Bases and Strongly Koszul Toric Rings

  • Kazunori Matsuda
  • Hidefumi Ohsugi

Abstract

Restuccia and Rinaldo proved that a standard graded $K$-algebra $K[x_1,\dots,x_n]/I$ is strongly Koszul if the reduced Gröbner basis of $I$ with respect to any reverse lexicographic order is quadratic. In this paper, we give a sufficient condition for a toric ring $K[A]$ to be strongly Koszul in terms of the reverse lexicographic Gröbner bases of its toric ideal $I_A$. This is a partial extension of a result given by Restuccia and Rinaldo.

In addition, we show that any strongly Koszul toric ring generated by squarefree monomials is compressed. Using this fact, we show that our sufficient condition for $K[A]$ to be strongly Koszul is both necessary and sufficient when $K[A]$ is generated by squarefree monomials.

Published
2016-11-01
How to Cite
Matsuda, K., & Ohsugi, H. (2016). Reverse Lexicographic Gröbner Bases and Strongly Koszul Toric Rings. MATHEMATICA SCANDINAVICA, 119(2), 161-168. https://doi.org/10.7146/math.scand.a-24741
Section
Articles