Skeletons of stable maps II: superabundant geometries
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40687_2017_Article_101.pdf
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776.49 KB
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Author(s)
Ranganathan, Dhruv
Date Issued
June 2017
Journal
Research in the Mathematical Sciences
Publisher
Springer International Publishing
Citation
Ranganathan, Dhruv. “Skeletons of Stable Maps II: Superabundant Geometries.” Research in the Mathematical Sciences 4.1 (2017): n. pag.
Version
Final published version
Abstract
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 three 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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution
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DOI of Published Version
https://doi.org/10.1186/s40687-017-0101-5
