Log-Canonical Rings of Graph Curves

by William Baker

Institution: Emory University
Year: 2016
Keywords: Mathematics; Canonical Ring; Graph Curve; Stable Curve
Posted: 02/05/2017
Record ID: 2102397
Full text PDF: http://pid.emory.edu/ark:/25593/rjnm9


I generalize David Zureick-Brown and John Voight's work on log-canonical rings to graph curves. I use a paper of Noot as a starting point. I outline some of the difficulties in developing Max Noether-like and Petri-like theorems. I work out theorems for the generators of most well behaved graph curves. I also find a useful construction for hyperelliptic graph curves. Introduction - 1  – Noneffective canoincal divisors and bridges - 2  – Inductive Step - 3  – One point log divisors - 3  – Two point log divisors - 4  – Three point log divisors - 5  – Hyper Elliptic Curves - 5 Advisors/Committee Members: Raman, Parimala (Committee Member), Allison, Blake A (Committee Member), Zureick-Brown, David M (Thesis Advisor).