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Cross-ratio degrees and perfect matchings.

Authors :
Silversmith, Rob
Source :
Proceedings of the American Mathematical Society; Dec2022, Vol. 150 Issue 12, p5057-5072, 16p
Publication Year :
2022

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. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
00029939
Volume :
150
Issue :
12
Database :
Complementary Index
Journal :
Proceedings of the American Mathematical Society
Publication Type :
Academic Journal
Accession number :
159596642
Full Text :
https://doi.org/10.1090/proc/16016