Limit linear series and the Amini–Baker construction

Abstract

We draw comparisons between the author’s recent construction of limit linear series for curves not of compact type and the Amini–Baker theory of limit linear series on metrized complexes, as well as the related theories of divisors on discrete graphs and on metric graphs. From these we conclude that the author’s theory (like the others) satisfies the Riemann and Clifford inequalities. Motivated by our comparisons, we also develop negative results on Brill–Noether generality for certain families of metric graphs. Companion work of He develops our comparisons further and uses them to prove new results on smoothability of Amini–Baker limit linear series and of divisors on metric graphs.