On the set of Chern numbers in local rings

2022/06/10 by Hoang Le Truong, Truong, Hoang Le, Hoang Ngoc Yen +1
Mathematics · #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2206.04856

openalex publication_date 2022/06/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper purposes to characterize Noetherian local rings (R, \mathfrakm) such that the Chern numbers of certain \mathfrakm-primary ideals in R bounded above or range among only finitely many values. Consequently, we characterize the Gorensteinness, Cohen-Macaulayness, generalized Cohen-Macaulayness of local rings in terms of the behavior of its Chern numbers.

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