Acta Mathematica Vietnamica
Ulrich Ideals on Rational Triple Points of Dimension Two
Kyosuke Maeda
,
Ken-ichi Yoshida
Abstract
In this paper, we prove that the canonical trace ideal ${\text {trace}}_A(\omega _A)$ is an Ulrich ideal for any two-dimensional rational triple point $A$. Using this, we classify all Ulrich ideals on rational triple points. Moreover, we show that if $(A,{\mathfrak m})$ is a two-dimensional quotient singularity with the multiplicity $e \ge 4$, then ${\mathfrak m}$ is the unique Ulrich ideal of $A$. As a result, we can classify all Ulrich ideals of $A$ if $A$ is either a rational triple point or a quotient singularity.
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