Gorensteinness for normal tangent cones of elliptic ideals

Abstract

Let A be a two-dimensional excellent normal Gorenstein local domain. In this paper, we characterize elliptic ideals $I\subset A$ for its normal tangent cone $\bar{G}\left(I\right)$ to be Gorenstein. Moreover, we classify all those ideals in a Gorenstein elliptic singularity in the characteristic zero case.