Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
134 tokens/sec
GPT-4o
10 tokens/sec
Gemini 2.5 Pro Pro
47 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

On $p_g$-ideals (1808.09130v1)

Published 28 Aug 2018 in math.AC

Abstract: Let $(A,\mathfrak{m})$ be an excellent normal domain of dimension two. We define an $\mathfrak{m}$-primary ideal $I$ to be a $p_g$-ideal if the Rees algebra $A[It]$ is a Cohen-Macaulay normal domain. When $A$ contains an algebraically closed field $k \cong A/\mathfrak{m}$ then Okuma, Watanabe and Yoshida proved that $A$ has $p_g$-ideals and furthermore product of two $p_g$-ideals is a $p_g$ ideal. In this article we show that if $A$ is an excellent normal domain of dimension two containing a field $k \cong A/\mathfrak{m}$ of characteristic zero then also $A$ has $p_g$-ideals. Furthermore product of two $p_g$-ideals is $p_g$.

Summary

We haven't generated a summary for this paper yet.