A canonical polytopal resolution for transversal monomial ideals

Abstract

Let $S=k[x_{11},\cdots ,x_{1b_1},\cdots ,x_{n1},\cdots ,x_{n{b}_n}]$ be a polynomial ring in $m=b_1+\cdots +b_n$ variables over a field $k$. For all $j$, $1\le j\le n$, let $P_j$ be the prime ideal generated by variables $\{x_{j1},\cdots ,x_{j{b}_j}\}$ and let $$I_{n,t}=\sum _{1\le j_1<\cdots <j_t\le n}{P}_{j_1}\dots P_{j_t}$$ be the transversal monomial ideal of degree $t$ on $P_1,\cdots ,P_n$. We explicitly construct a canonical polytopal ${\mathbb{Z}}^t$-graded minimal free resolution for the ideal $I_{n,t}$ by means of suitable gluing of polytopes.

11 pages, 1 figure

References in corpus (2)

• Cellular resolutions of Cohen-Macaulay monomial quotient rings
• Cellular resolutions of powers of monomial ideals