In:
Nagoya Mathematical Journal, Cambridge University Press (CUP), Vol. 248 ( 2022-12), p. 779-800
Abstract:
Let $(A,\mathfrak m)$ be an excellent two-dimensional normal local domain. In this paper, we study the elliptic and the strongly elliptic ideals of A with the aim to characterize elliptic and strongly elliptic singularities, according to the definitions given by Wagreich and Yau. In analogy with the rational singularities, in the main result, we characterize a strongly elliptic singularity in terms of the normal Hilbert coefficients of the integrally closed $\mathfrak m$ -primary ideals of A . Unlike $p_g$ -ideals, elliptic ideals and strongly elliptic ideals are not necessarily normal and necessary, and sufficient conditions for being normal are given. In the last section, we discuss the existence (and the effective construction) of strongly elliptic ideals in any two-dimensional normal local ring.
Type of Medium:
Online Resource
ISSN:
0027-7630
,
2152-6842
Language:
English
Publisher:
Cambridge University Press (CUP)
Publication Date:
2022
detail.hit.zdb_id:
2186888-8
SSG:
17,1
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