Comparing invariants of toric ideals of bipartite graphs

Abstract

Let $G$ be a finite simple graph and let $I_G$ denote its associated toric ideal in the polynomial ring $R$. For each integer $n\ge 2$, we completely determine all the possible values for the tuple $(\mathrm{reg}(R/I_G),\mathrm{deg}(h_{R/I_G}(t)),\mathrm{pdim}(R/I_G),\mathrm{depth}(R/I_G),\dim (R/I_G))$ when $G$ is a connected bipartite graph on $n$ vertices.

14 pages, updated references and added Remark 2.12, comments welcome