Saturation bounds for smooth varieties

Abstract: 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.

commutative algebra

Audience: researchers in the topic

Fellowship of the Ring

Series comments: Description: National Commutative Algebra Seminar

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