2016/09/30 by Dhruv Ranganathan · 1 citation
Mathematics · #math.AG
published as Research in the Mathematical Science (2017) 4:11 · 17 pages, 1 figure. v2 fixes a minor gap in the proof of Theorem D and adds details to the construction of the skeleton of a toroidal Artin stack. Minor clarifications throughout. To appear in Research in the Mathematical Sciences
arxiv created 2017/02/24 · arxiv updated 2017/06/27
We implement new techniques involving Artin fans to study the realizability of tropical stable maps in superabundant combinatorial types. Our approach is to understand the skeleton of a fundamental object in logarithmic Gromov--Witten theory -- the stack of prestable maps to the Artin fan. This is used to examine the structure of the locus of realizable tropical curves and derive 3 principal consequences. First, we prove a realizability theorem for limits of families of tropical stable maps. Second, we extend the sufficiency of Speyer's well-spacedness condition to the case of curves with good reduction. Finally, we demonstrate the existence of liftable genus 1 superabundant tropical curves that violate the well-spacedness condition.