Canonical rings of Q-divisors
Evan O'Dorney (Harvard)
Saturday, 7 February 2015, 1:55 PM
MIT, 56-169
Certain questions in the theory of algebro-geometric stacks and of modular forms lead to problems concerning the canonical ring S = ⊕_{k≥0} H^0(X,kD) of a curve X associated to a Q-divisor D (a formal linear combination of points with rational coefficients). For the simplest curve X = P^1, the projective line, these become easily stated problems about rational functions. In this talk, I will present my findings on this topic at the Emory REU, namely a complete description of the ring S when D has at most two points, a general bound on its generators and relations, and results on how S varies when the points of D move while their coefficients remain fixed.