UC Berkeley

Commutative Algebra and Algebraic Geometry Seminar

October 10, 2017

939 Evans Hall

3:45PM: Serre Condition (S_r) for Simplicial Complexes

Brent Holmes

For a fixed integer r, Serre's condition (S_r) is a condition on the depth of a ring at various localizations. It can be viewed as a weakening of the Cohen-Macaulay condition. In this talk, we focus on Serre's condition for Stanley-Reisner rings. The first main topic will be the relationship between Serre's (S_2) condition and Hirsch type bounds on the diameter of the dual graph. The second topic is some homological properties of Stanley-Reisner rings with (S_r) condition using higher nerves.

5:00PM: No seminar



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