Details

Autor(en) / Beteiligte

• OKUMA, TOMOHIRO
• ROSSI, MARIA EVELINA
• WATANABE, KEI-ICHI
• YOSHIDA, KEN-ICHI

Titel

NORMAL HILBERT COEFFICIENTS AND ELLIPTIC IDEALS IN NORMAL TWO-DIMENSIONAL SINGULARITIES

Ist Teil von

• Nagoya mathematical journal, 2022-12, Vol.248, p.779-800

Ort / Verlag

Cambridge, UK: Cambridge University Press

Erscheinungsjahr

2022

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• 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.