Vol. 16, No. 6, 2022

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Saturation bounds for smooth varieties

Lawrence Ein, Huy Tài Hà and Robert Lazarsfeld

Vol. 16 (2022), No. 6, 1531–1546
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