Gorensteinness for normal tangent cones of elliptic ideals

TL;DR

This paper characterizes when the normal tangent cone of elliptic ideals in a 2D Gorenstein local domain is Gorenstein, providing a classification in elliptic singularities over characteristic zero.

Contribution

It offers a characterization of Gorensteinness for tangent cones of elliptic ideals and classifies such ideals in Gorenstein elliptic singularities in characteristic zero.

Findings

Normal tangent cone of elliptic ideals can be Gorenstein under specific conditions.

Complete classification of elliptic ideals with Gorenstein tangent cones in elliptic singularities.

Results are specific to characteristic zero cases.

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 $\overline{G}(I)$ to be Gorenstein. Moreover, we classify all those ideals in a Gorenstein elliptic singularity in the characteristic zero case.