Eloísa Grifo : A stable version of Harbourne's Conjecture

Posted by Wenliang Zhang , part of the Commutative Algebra Seminar.

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Nov. 1, 2019, 2 p.m.

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Abstract

The powers of an ideal are easy to compute, though difficult to describe geometrically; in contrast, symbolic powers are difficult to compute while having a natural geometric description. In trying to compare symbolic and ordinary powers, Harbourne conjectured that a famous containment by Ein--Lazersfeld--Smith, Hochster--Huneke, and Ma--Schwede could be tightened. Harbourne's Conjecture is a statement depending on n that unfortunately has been disproved for particular values of n. However, recent evidence points towards a stable version of Harbourne's conjecture, where we ask only for n to be large enough. Some of that evidence is joint work with Craig Huneke and Vivek Mukundan.