Benjamin Mudrak

Purdue University

Gorenstein Linkage of m-Primary Monomial Ideals

Consider the polynomial ring $R = k[x_1,…,x_n]$ where $k$ is a field. Let $\mathfrak{m} = (x_1,…,x_n)$ and $I$ be an $\mathfrak{m}$-primary monomial ideal in $R$. We consider the problem of determining whether such ideals are in the Gorenstein liasion class of a complete intersection (glicci). We prove that all $\mathfrak{m}$-primary monomial ideals in $k[x,y,z]$ with at most 8 minimal generators are homogeneously glicci and construct a large class of $\mathfrak{m}$-primary monomial ideals in $k[x_1,…,x_n]$ for any $n$ with any number of minimal generators that are homogeneously glicci but not in the complete intersection liaison class of a complete intersection (licci). All Gorenstein-links used are constructed explicitly and every second step links to another $\mathfrak{m}$-primary monomial ideal.