Alladi Ramakrishnan Hall

Gorenstein Monomial Curves

Hema Srinivasan

University of Missouri

We discuss the problem of finding the structure and resolutions of Gorenstein Monomial Curves. We will explicitly give the structure up to embedding dimension four. In higher dimension we show some partial results for both decomposable and indecomposable Gorenstein monomial curves. A monomial curve in $A^n$ is determined by a set of $n$ relatively prime positive integers $A = \{ a_1, \ldots, , a_n\}$. We will construct a partial invariant, called a principal matrix of $D(A)$ which determines the structure of all Gorenstein monomial curves in $A^4$ and some in $A^5$. In addition, when the integers in $A$ are in arithmetic progression, the Gorenstein monomial curve associated to $A$ has a particularly attractive and elegant resolution. There are several open questions in this subject.