Lech's inequality can be sharpened uniformly

Abstract: The classical Lech's inequality can be viewed as a uniform, independent of an ideal, upper bound on the ratio of the multiplicity and the colength of an m-primary ideal of a local ring. It was also observed by Lech that, if the dimension is at least two, it is not sharp for any given ideal. Recently, we were able to show more: most of the time, it is possible to improve Lech's upper bound so that it works for all ideals. I will present the proof of this result and all required background in multiplicity theory.

Mathematics

Audience: advanced learners

( paper )

IIT Bombay Virtual Commutative Algebra Seminar

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