Divisors on graphs, connected flags, and syzygies

Combinatorics Seminar
Friday, October 12, 2012 - 3:05pm
1 hour (actually 50 minutes)
Skiles 005
Georgia Tech
Associated to every finite graph G there is a canonical ideal which encodes the linear equivalences of divisors on G. We study this ideal and its associated initial ideal. We give an explicit description of their syzygy modules and the Betti numbers in terms of the "connected flags" of G. This resolves open questions posed by Postnikov-Shapiro, Perkinson-Perlmen-Wilmes, and Manjunath-Sturmfels. No prior knowledge in advanced commutative algebra will be assumed. This is a joint work with Fatemeh Mohammadi.