Good ideals and $p_g$-ideals in two-dimensional normal singularities
Commutative Algebra
2025-12-16 v2 Algebraic Geometry
Abstract
In this paper, we introduce the notion of -ideals and -cycles, which inherits nice properties of integrally closed ideals on rational singularities. As an application, we prove an existence of good ideals for two-dimensional Gorenstein normal local rings. Moreover, we classify all Ulrich ideals for two-dimensional simple elliptic singularities with small degree.
Keywords
Cite
@article{arxiv.1407.1590,
title = {Good ideals and $p_g$-ideals in two-dimensional normal singularities},
author = {Tomohiro Okuma and Kei-ichi Watanabe and Ken-ichi Yoshida},
journal= {arXiv preprint arXiv:1407.1590},
year = {2025}
}
Comments
21 pages. The proof of Proposition 5.6 of the first version has been revised