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Lech’s inequality and stability of local rings

CMSA EVENTS: CMSA Algebra Seminar

When: October 16, 2025
2:00 pm - 3:00 pm
Where: CMSA, 20 Garden St, G10
Address: 20 Garden Street, Cambridge, MA 02138, United States
Speaker: Linquan Ma (Purdue University)

We explore Lech’s inequality relating the colength and multiplicity of m-primary ideals in a Noetherian local ring (R,m). We introduce a natural invariant that measures the sharpness of Lech’s inequality and show its connections with singularities of asymptotically semistable varieties and singularities arising from the MMP. We compute this invariant in various examples. This is joint work with Ilya Smirnov.