Ulrich ideals on rational triple points of dimension two

2025/07/17 by Maeda, Kyosuke, Yoshida, Ken-ichi · 1 citation
#13H10 #14B05 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2507.12980

Abstract

In this paper, we prove the canonical trace ideal trace(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, m) is a two-dimensional quotient singularity with the multiplicity e ≥ 4 then 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.

Citations

• A Geometric description of almost Gorensteinness for two-dimensional normal singularities
• On generalized Gorenstein local rings
• Ulrich ideals and almost Gorenstein rings
• Good ideals and p_g-ideals in two-dimensional normal singularities
• Ulrich ideals and modules over two-dimensional rational singularities
• Ulrich ideals and modules

Cited by

• Nearly Gorenstein rational surface singularities

Related

• Ulrich ideals and modules over two-dimensional rational singularities
• The Structure of Ulrich ideals in hypersurfaces
• Good ideals and p_g-ideals in two-dimensional normal singularities
• The structure of chains of Ulrich ideals in Cohen-Macaulay local rings of dimension one
• On the theory of generalized Ulrich modules