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Cross-Ratio degrees and perfect matchings
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Silversmith, Robert (2022) Cross-Ratio degrees and perfect matchings. Proceedings of the American Mathematical Society, 150 . pp. 5057-5072. doi:10.1090/proc/16016 ISSN 0002-9939.
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Official URL: https://doi.org/10.1090/proc/16016
Abstract
Cross-ratio degrees count configurations of points
satisfying
cross-ratio constraints, up to isomorphism. These numbers arise in multiple contexts in algebraic and tropical geometry, and may be viewed as combinatorial invariants of certain hypergraphs. We prove an upper bound on cross-ratio degrees in terms of the theory of perfect matchings on bipartite graphs. We also discuss several of the many perspectives on cross-ratio degrees—including a connection to Gromov-Witten theory—and give many example computations.
| Item Type: | Journal Article | |||||||||
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| Subjects: | Q Science > QA Mathematics | |||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | |||||||||
| Library of Congress Subject Headings (LCSH): | Geometry, Algebraic , Moduli theory, Curves, Algebraic, Tropical geometry , Graph theory | |||||||||
| Journal or Publication Title: | Proceedings of the American Mathematical Society | |||||||||
| Publisher: | American Mathematical Society | |||||||||
| ISSN: | 0002-9939 | |||||||||
| Official Date: | 23 September 2022 | |||||||||
| Dates: |
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| Volume: | 150 | |||||||||
| Page Range: | pp. 5057-5072 | |||||||||
| DOI: | 10.1090/proc/16016 | |||||||||
| Status: | Peer Reviewed | |||||||||
| Publication Status: | Published | |||||||||
| Reuse Statement (publisher, data, author rights): | First published in Proceedings of the American Mathematical Society in [volume/issue number and year], published by the American Mathematical Society,” and the copyright notice in proper form must be placed on all copies. | |||||||||
| Access rights to Published version: | Restricted or Subscription Access | |||||||||
| Copyright Holders: | © Copyright 2022 American Mathematical Society | |||||||||
| Date of first compliant deposit: | 13 April 2022 | |||||||||
| Date of first compliant Open Access: | 14 April 2022 | |||||||||
| RIOXX Funder/Project Grant: |
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