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Seminar

Fellowship of the Ring, National Seminar: Saturation bounds for smooth varieties March 04, 2021 (01:30 PM PST - 03:00 PM PST)
Parent Program: --
Location: MSRI: Online/Virtual
Speaker(s) Robert Lazarsfeld (State University of New York, Stony Brook)
Description

To attend this seminar, you must register in advance, by clicking HERE.

Video

Saturation Bounds for Smooth Varieties

Abstract/Media

To attend this seminar, you must register in advance, by clicking HERE.

Let X be a smooth complex projective variety with homogeneous ideal I. We consider the question of bounding the saturation degree of the powers I^a of I, ie the degrees

after which this power agrees with the symbolic power I^(a). I’ll discuss joint work with Lawrence Ein and Tai Huy Ha giving results in two situations:

—    When I is the ideal of a smooth curve C, we give a bound in terms of the regularity of C, extending results of Geramita et al, Sidman, Chandler and others in the case of finite sets;

—    When X is smooth of arbitrary dimension, we give a bound in terms of the degrees of defining equations that has the same general shape as (but a rather different proof

than) regularity bounds established many years ago with Bertram and Ein.



I will also discuss a number of open questions.

Asset no preview Notes 5.89 MB application/pdf

Saturation Bounds for Smooth Varieties