Seminar
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| Location: | SLMath: Online/Virtual |
To attend this seminar, you must register in advance, by clicking HERE.
Saturation Bounds for Smooth Varieties
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.
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Notes
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