Fitting Ideals without a Presentation

2025/01/19 by Sharland, Ayse, Smith, Jacob
#58K20 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2501.11100

Abstract

In this article, we investigate alternative construction of Fitting ideals of pushforward modules f_*O_X,0 for finite and holomorphic map-germs from an n-dimensional Cohen-Macaulay space (X,0) to (ℂⁿ⁺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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