Seminar

Commutative Algebra and Algebraic Geometry

      Tuesdays, 3:45-6pm in Evans 939

        organizer: David Eisenbud

        http://hosted.msri.org/alg 

Date: Oct 21

3:45 Volkmar Welker: Betti numbers of barycentric and edgewise subdivisions

(joint with Aldo Conca and Martina Kubitzke)

We prove that syzygies of Stanley-Reisner rings of under iterated barycentric subdivisions and edgewise subdivisions exhibit a similar behavior as syzygies of algebraic varieties under high Veronese embeddings (see the work of Ein, Lazarsfeld and Erman and Zhou).

These two combinatorial operations on simplical complexes have some formal similarity (but also some important dissimilarity) with the formation of the Veronese subalgebras.

In particular, the edgewise subdivision of a simplicial complex is closely related, via initial ideals, with the formation of Veronese subalgebras of the associated Stanley-Reisner ring, but this relation together with the results of Ein et. al. and Zou imply only some fraction of the nonvanishing of syzygies of edgewise subdivisions derived in our work.

5:00 NO 5pm TALK THIS WEEK