Products and powers of principal symmetric ideals

Eric Dannetun, Riccardo Formenti, Bo Y. Gao, Juliann Geraci, Ross Kogel, Yuelin Li, Shreya Mandal, Vinuge Rupasinghe,Alexandra Seceleanu, Duc Van Khank Tran, Noah Walker

arxiv(2024)

引用 0|浏览0
暂无评分
摘要
Principal symmetric ideals were recently introduced by Harada, Seceleanu, and Sega, with a focus on their homological properties. They are ideals generated by the orbit of a single polynomial under permutations of variables in a polynomial ring. In this paper we seek to determine when a product of two principal symmetric ideals is principal symmetric and when all the powers of a principal symmetric ideal are again principal symmetric ideals. We characterize the ideals that have the latter property as being generated by polynomials invariant up to a scalar multiple under permutation of variables. Recognizing principal symmetric ideals is an open question for the purpose of which we produce certain obstructions. We also demonstrate that the Hilbert functions of symmetric monomial ideals are not all given by symmetric monomial ideals, in contrast to the non-symmetric case.
更多
查看译文
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要