Toward Free Resolutions Over Scrolls

Abstract

Let $R=k[x]/I$ where $I$ is the defining ideal of a rational normal $k$-scroll. We compute the Betti numbers of the ground field $\mathbb{k}$ as a module over $R$. For $k=2$, we give the minimal free resolution of $\mathbb{k}$ over $R$.

14 pages, 2 figures