Length, multiplicity, and multiplier ideals期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

按检索

Length, multiplicity, and multiplier ideals

Authors:	Tommaso de Fernex

Institution:	Department of Mathematics, University of Michigan, East Hall, 525 East University Avenue, Ann Arbor, Michigan 48109-1109

Abstract:	Let $(R,\mathfrak{m})$ be an -dimensional regular local ring, essentially of finite type over a field of characteristic zero. Given an $\mathfrak{m}$ -primary ideal $\mathfrak{a}$ of , the relationship between the singularities of the scheme defined by $\mathfrak{a}$ and those defined by the multiplier ideals $\mathcal{J}(\mathfrak{a}^c)$ , with varying in $\mathbb{Q}_+$ , are quantified in this paper by showing that the Samuel multiplicity of $\mathfrak{a}$ satisfies $e(\mathfrak{a}) \ge (n+k)^n/c^n$ whenever $\mathcal{J}(\mathfrak{a}^c) \subseteq \mathfrak{m}^{k+1}$ . This formula generalizes an inequality on log canonical thresholds previously obtained by Ein, Mustata and the author of this paper. A refined inequality is also shown to hold for small dimensions, and similar results valid for a generalization of test ideals in positive characteristics are presented.

Keywords:	Multiplier ideal Samuel multiplicity monomial ideal

	点击此处可从《Transactions of the American Mathematical Society》浏览原始摘要信息
	点击此处可从《Transactions of the American Mathematical Society》下载免费的PDF全文