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arXiv · 2501.11100

Fitting Ideals without a Presentation

Ayse Sharland·Jacob Smith
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Abstract

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.

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Ayse Sharland, Jacob Smith. 2025-01-19. Fitting Ideals without a Presentation. https://arxiv.org/abs/2501.11100

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