Acta Mathematica Vietnamica
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On the Set of Chern Numbers in Local Rings
Le Truong Hoang , Ngoc Yen Hoangpp. 139-157
Abstract
The purpose of this paper is to characterize Noetherian local rings $(R, \mathfrak {m})$ such that the Chern numbers of certain $\mathfrak {m}$-primary ideals in $R$ are bounded above or range among only finitely many values. Consequently, we characterize the Gorensteinness, Cohen-Macaulayness, and generalized Cohen-Macaulayness of local rings in terms of the behavior of their Chern numbers.