Cross-ratio degrees and perfect matchings
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Abstract:
Cross-ratio degrees count configurations of points $z_1,\ldots ,z_n\in \mathbb {P}^1$ satisfying $n-3$ 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.References
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Additional Information
- Rob Silversmith
- Affiliation: Warwick Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom
- MR Author ID: 936729
- ORCID: 0000-0003-0508-5958
- Email: Rob.Silversmith@warwick.ac.uk
- Received by editor(s): July 30, 2021
- Received by editor(s) in revised form: January 24, 2022
- Published electronically: September 23, 2022
- Additional Notes: This project was supported by NSF Grant DMS-1645877, and by a Zelevinsky Postdoctoral Fellowship at Northeastern University.
- Communicated by: Rachel Pries
- © Copyright 2022 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 150 (2022), 5057-5072
- MSC (2020): Primary 14N10, 14H10, 14T15, 05C30
- DOI: https://doi.org/10.1090/proc/16016