Special Divisors on Marked Chains of Cycles

Abstract:  One area of current research in algebraic geometry is whether it is possible to classify all divisors on an algebraic curve. In general, this is a difficult question, but it turns out that the chain of loops has enough combinatorial structure that some progress can be made. In 2012, Cools, Draisma, Payne, and Robeva classified divisors on a generic chain of loops, and in 2016, Pflueger generalized their techniques to classify divisors on an arbitrary chain of loops. We will discuss Pflueger's techniques and results, focusing on this classification. No prior knowledge of algebraic geometry is assumed.