#### Date of Award

2018

#### Document Type

Open Access Dissertation

#### Department

Mathematics

#### Sub-Department

College of Arts and Sciences

#### First Advisor

Andrew Kustin

#### Abstract

Let S be a set of four variables, k a field of characteristic not equal to two such that k contains all square roots, and I a height four Gorenstein ideal of k[S] generated by nine quadratics so that I has a Gorenstein-linear resolution. We define a complex X• so that each module of X• is the tensor product of a certain polynomial ring Q in nine variables and a direct sum of indecomposable k[Sym(S)]-modules and the differential maps are Q- and k[Sym(S)]-module homomorphisms. Work with the Macaulay2 software suggests that H0(X•) is the special fiber ring of I and H1(X•) = 0.

#### Recommended Citation

Hudson, J.(2018). *Special Fiber Rings of Certain Height Four Gorenstein Ideals.* (Doctoral dissertation). Retrieved from https://scholarcommons.sc.edu/etd/4782