Reverse lexicographic Gröbner bases and strongly Koszul toric rings

Abstract

Restuccia and Rinaldo proved that a standard graded $K$-algebra $K[x_1,...x_n]/I$ 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.

7 pages, the title and abstract corrected

References in corpus (2)

• Linear flags and Koszul filtrations
• Strong Koszulness of toric rings associated with stable set polytopes of trivially perfect graphs

Cited by in corpus (1)

• Non-Koszul quadratic Gorenstein toric rings