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Let $A$ be a two-dimensional excellent normal Gorenstein local domain. Inthis paper, we characterize elliptic ideals $I \subset A$ for its normaltangent cone $\overline{G}(I)$ to be Gorenstein. Moreover, we classify allthose ideals in a Gorenstein elliptic singularity in the characteristic zerocase.

Gorensteinness for normal tangent cones of elliptic ideals