CONSTANCY OF THE HILBERT-SAMUEL FUNCTION

被引：0

作者：

Cossart, Vincent ^{[1
]}

Piltant, Olivier ^{[1
]}

Schober, Bernd ^{[2
]}

机构：

[1] Univ Paris Saclay, Lab Math Versailles LMV UMR 8100, 45 Ave Etats Unis, F-78035 Versailles, France

[2] Carl von Ossietzky Univ Oldenburg, Inst Math, D-26111 Oldenburg, Germany

来源：

NAGOYA MATHEMATICAL JOURNAL | 2024年

关键词：

excellent schemes; Hilbert-Samuel function; singularities; resolution of singularities; ALGEBRAIC-VARIETIES; SINGULARITIES; RESOLUTION;

D O I：

10.1017/nmj.2024.13

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove a criterion for the constancy of the Hilbert-Samuel function for locally Noetherian schemes such that the local rings are excellent at every point. More precisely, we show that the Hilbert-Samuel function is locally constant on such a scheme if and only if the scheme is normally flat along its reduction and the reduction itself is regular. Regularity of the underlying reduced scheme is a significant new property.

引用

页数：15

共 50 条

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