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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Online-Zugang: | https://arxiv.org/abs/2501.11100 |
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| _version_ | 1866912194110685184 |
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| author | Sharland, Ayse Smith, Jacob |
| author_facet | Sharland, Ayse Smith, Jacob |
| contents | In this article, we investigate alternative construction of Fitting ideals of pushforward modules $f_*\mathcal{O}_{X,0}$ for finite and holomorphic map-germs from an $n$-dimensional Cohen-Macaulay space $(X,0)$ to $(\mathbb{C}^{n+1},0)$. For corank 1 map-germs, we generalize a result of D. Mond and R. Pellikaan to iteratively calculate $k$-th Fitting ideals as ideal quotients of lower ones. We also show that for a stable map-germ of any corank, the first Fitting ideal can be calculated as a quotient ideal of the Jacobian of the image and the pushforward of the ramification ideal, which is a modification of classical result of due to Piene. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_11100 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fitting Ideals without a Presentation Sharland, Ayse Smith, Jacob Commutative Algebra Algebraic Geometry 58K20 In this article, we investigate alternative construction of Fitting ideals of pushforward modules $f_*\mathcal{O}_{X,0}$ for finite and holomorphic map-germs from an $n$-dimensional Cohen-Macaulay space $(X,0)$ to $(\mathbb{C}^{n+1},0)$. For corank 1 map-germs, we generalize a result of D. Mond and R. Pellikaan to iteratively calculate $k$-th Fitting ideals as ideal quotients of lower ones. We also show that for a stable map-germ of any corank, the first Fitting ideal can be calculated as a quotient ideal of the Jacobian of the image and the pushforward of the ramification ideal, which is a modification of classical result of due to Piene. |
| title | Fitting Ideals without a Presentation |
| topic | Commutative Algebra Algebraic Geometry 58K20 |
| url | https://arxiv.org/abs/2501.11100 |