Ulrich ideals on rational triple points of dimension two
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911061326692352 |
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| author | Maeda, Kyosuke Yoshida, Ken-ichi |
| author_facet | Maeda, Kyosuke Yoshida, Ken-ichi |
| contents | 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 \ge 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_12980 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Ulrich ideals on rational triple points of dimension two Maeda, Kyosuke Yoshida, Ken-ichi Commutative Algebra 13H10, 14B05 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 \ge 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. |
| title | Ulrich ideals on rational triple points of dimension two |
| topic | Commutative Algebra 13H10, 14B05 |
| url | https://arxiv.org/abs/2507.12980 |