Regularity and h-polynomials of toric ideals of graphs
Abstract
For all integers $4 \leq r \leq d$, we show that there exists a finite simple graph $G= G_{r,d}$ with toric ideal $I_G \subset R$ such that $R/I_G$ has (Castelnuovo-Mumford) regularity $r$ and $h$-polynomial of degree $d$. To achieve this goal, we identify a family of graphs such that the graded Betti numbers of the associated toric ideal agree with its initial ideal, and furthermore, this initial ideal has linear quotients. As a corollary, we can recover a result of Hibi, Higashitani, Kimura, and O'Keefe that compares the depth and dimension of toric ideals of graphs.
- Publication:
-
arXiv e-prints
- Pub Date:
- March 2020
- DOI:
- 10.48550/arXiv.2003.07149
- arXiv:
- arXiv:2003.07149
- Bibcode:
- 2020arXiv200307149F
- Keywords:
-
- Mathematics - Commutative Algebra;
- Mathematics - Algebraic Geometry;
- 13D02;
- 13P10;
- 13D40;
- 14M25;
- 05E40