Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring: Serre Condition \(S_r\) for Simplicial Complexes

Seminar | October 10 | 3:45-4:45 p.m. | 939 Evans Hall

 Brent Holmes, University of Kansas

 Department of Mathematics

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.