Saturation bounds for smooth varieties

Lawrence Ein; Huy Tài Hà; Robert Lazarsfeld

doi:10.2140/ant.2022.16.1531

Saturation bounds for smooth varieties

Lawrence Ein
, Huy Tài Hà
, Robert Lazarsfeld

Mathematics

University of Illinois at Chicago
Tulane University

Research output: Contribution to journal › Article › peer-review

Abstract

We prove bounds on the saturation degrees of homogeneous ideals (and their powers) defining smooth complex projective varieties. For example, we show that a classical statement due to Macaulay for zero-dimensional complete intersection ideals holds for any smooth variety. For curves, we bound the saturation degree of powers in terms of the regularity.

Original language	English
Pages (from-to)	1531-1546
Number of pages	16
Journal	Algebra and Number Theory
Volume	16
Issue number	6
DOIs	https://doi.org/10.2140/ant.2022.16.1531
State	Published - 2022

Keywords

Castelnuovo–Mumford regularity
saturation degree
symbolic powers of ideals

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10.2140/ant.2022.16.1531

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title = "Saturation bounds for smooth varieties",

abstract = "We prove bounds on the saturation degrees of homogeneous ideals (and their powers) defining smooth complex projective varieties. For example, we show that a classical statement due to Macaulay for zero-dimensional complete intersection ideals holds for any smooth variety. For curves, we bound the saturation degree of powers in terms of the regularity.",

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author = "Lawrence Ein and H{\`a}, \{Huy T{\`a}i\} and Robert Lazarsfeld",

year = "2022",

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AU - Ein, Lawrence

AU - Hà, Huy Tài

AU - Lazarsfeld, Robert

PY - 2022

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AB - We prove bounds on the saturation degrees of homogeneous ideals (and their powers) defining smooth complex projective varieties. For example, we show that a classical statement due to Macaulay for zero-dimensional complete intersection ideals holds for any smooth variety. For curves, we bound the saturation degree of powers in terms of the regularity.

KW - Castelnuovo–Mumford regularity

KW - saturation degree

KW - symbolic powers of ideals

UR - https://www.scopus.com/pages/publications/85140228880

U2 - 10.2140/ant.2022.16.1531

DO - 10.2140/ant.2022.16.1531

M3 - Article

AN - SCOPUS:85140228880

SN - 1937-0652

VL - 16

SP - 1531

EP - 1546

JO - Algebra and Number Theory

JF - Algebra and Number Theory

IS - 6

ER -

Saturation bounds for smooth varieties

Abstract

Keywords

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