Saturation bounds for smooth varieties

Ein, Lawrence; Hà, Huy Tài; Lazarsfeld, Robert

doi:10.2140/ant.2022.16.1531

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Saturation bounds for smooth varieties

Lawrence Ein, Huy Tài Hà and Robert Lazarsfeld

Vol. 16 (2022), No. 6, 1531–1546

DOI: 10.2140/ant.2022.16.1531

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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Keywords

saturation degree, symbolic powers of ideals, Castelnuovo–Mumford regularity

Mathematical Subject Classification

Primary: 13B02, 14F99

Milestones

Received: 2 April 2021

Revised: 13 July 2021

Accepted: 5 October 2021

Published: 27 September 2022

Authors

Lawrence Ein
Department of Mathematics University of Illinois, Chicago Chicago, IL United States

Huy Tài Hà
Department of Mathematics Tulane University New Orleans, LA United States

Robert Lazarsfeld
Department of Mathematics Stony Brook University Stony Brook, NY United States

Vol. 16, No. 6, 2022