Skeletons of stable maps II: superabundant geometries
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...
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| Other Authors: | |
| Format: | Article |
| Language: | English |
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Springer International Publishing
2017
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| Online Access: | http://hdl.handle.net/1721.1/109948 |
| _version_ | 1826195261311942656 |
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| author | Ranganathan, Dhruv |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Ranganathan, Dhruv |
| author_sort | Ranganathan, Dhruv |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T10:10:15Z |
| format | Article |
| id | mit-1721.1/109948 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T10:10:15Z |
| publishDate | 2017 |
| publisher | Springer International Publishing |
| record_format | dspace |
| spelling | mit-1721.1/1099482022-09-26T16:12:13Z Skeletons of stable maps II: superabundant geometries Ranganathan, Dhruv Massachusetts Institute of Technology. Department of Mathematics Ranganathan, Dhruv 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. National Science Foundation (U.S.) (Grant CAREER DMS-1149054) 2017-06-16T15:08:12Z 2017-06-16T15:08:12Z 2017-06 2016-09 2017-06-01T03:45:11Z Article http://purl.org/eprint/type/JournalArticle 2197-9847 http://hdl.handle.net/1721.1/109948 Ranganathan, Dhruv. “Skeletons of Stable Maps II: Superabundant Geometries.” Research in the Mathematical Sciences 4.1 (2017): n. pag. en http://dx.doi.org/10.1186/s40687-017-0101-5 Research in the Mathematical Sciences Creative Commons Attribution http://creativecommons.org/licenses/by/4.0/ The Author(s) application/pdf Springer International Publishing Springer International Publishing |
| spellingShingle | Ranganathan, Dhruv Skeletons of stable maps II: superabundant geometries |
| title | Skeletons of stable maps II: superabundant geometries |
| title_full | Skeletons of stable maps II: superabundant geometries |
| title_fullStr | Skeletons of stable maps II: superabundant geometries |
| title_full_unstemmed | Skeletons of stable maps II: superabundant geometries |
| title_short | Skeletons of stable maps II: superabundant geometries |
| title_sort | skeletons of stable maps ii superabundant geometries |
| url | http://hdl.handle.net/1721.1/109948 |
| work_keys_str_mv | AT ranganathandhruv skeletonsofstablemapsiisuperabundantgeometries |