On the strong maximal rank conjecture in genus 22 and 23

Abstract

We develop new methods to study tropicalizations of linear series and show linear independence of sections. Using these methods, we prove two new cases of the strong maximal rank conjecture for linear series of degree 25 and 26 on curves of genus 22 and 23, respectively.

v2: title, abstract, and introduction revised to reflect a serious gap in the argument that these cases of the strong maximal rank conjecture imply that M_22 and M_23 are of general type; the body of the paper is unchanged