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Linkage of graphs with flows

Published: 18 July 2024 Publication History

Abstract

We prove several linkage properties of graphs with flows, generalizing some results on linkage of graphs. This translates in properties of connectedness through codimension one of certain posets. For example, the poset of flows and the posets of odd and even tropical spin curves. These posets are, respectively, the posets underlying the moduli space of roots of divisors on tropical curves and the moduli spaces of odd and even tropical spin curves.

References

[1]
Dan Abramovich, Lucia Caporaso, Sam Payne, The tropicalization of the moduli space of curves, Ann. Sci. Éc. Norm. Supér. (4) 48 (4) (2015) 765–809. MR 3377065.
[2]
Alex Abreu, Marco Pacini, The universal tropical Jacobian and the skeleton of the Esteves' universal Jacobian, Proc. Lond. Math. Soc. (3) 120 (3) (2020) 328–369. MR 4008373.
[3]
Alex Abreu, Marco Pacini, The resolution of the universal Abel map via tropical geometry and applications, Adv. Math. 378 (2021) 62 pp., MR 4184297.
[4]
Abreu, Alex; Pacini, Marco; Secco, Matheus (2022): On moduli spaces of roots in algebraic and tropical geometry. arXiv:2204.13471.
[5]
Lucia Caporaso, Geometry of tropical moduli spaces and linkage of graphs, J. Comb. Theory, Ser. A 119 (3) (2012) 579–598. MR 2871751.
[6]
Lucia Caporaso, Cinzia Casagrande, Maurizio Cornalba, Moduli of roots of line bundles on curves, Trans. Am. Math. Soc. 359 (8) (2007) 3733–3768. MR 2302513.
[7]
Lucia Caporaso, Margarida Melo, Marco Pacini, Tropicalizing the moduli space of spin curves, Sel. Math. New Ser. 26 (1) (2020) 44 pp., MR 4066537.
[8]
Dustin Cartwright, Sam Payne, Connectivity of tropicalizations, Math. Res. Lett. 19 (5) (2012) 1089–1095. MR 3039832.
[9]
Melody Chan, Søren Galatius, Sam Payne, Tropical curves, graph complexes, and top weight cohomology of M g, J. Am. Math. Soc. 34 (2) (2021) 565–594. MR 4280867.
[10]
Maurizio Cornalba, Moduli of curves and theta-characteristics, in: Lectures on Riemann Surfaces, Trieste, 1987, World Sci. Publ., Teaneck, NJ, 1989, pp. 560–589. MR 1082361.
[11]
Farkas, Gavril; Jensen, David; Payne, Sam (2020): The Kodaira dimensions of M ‾ 22 and M ‾ 23 . arXiv:2005.00622.
[12]
Allen Hatcher, William Thurston, A presentation for the mapping class group of a closed orientable surface, Topology 19 (3) (1980) 221–237. MR 579573.
[13]
Holmes, David; Molcho, Samuel; Pandharipande, Rahul; Pixton, Aaron; Schmitt, Johannes (2022): Logarithmic double ramification cycles. arXiv:2207.06778.
[14]
David Jensen, Dhruv Ranganathan, Brill-Noether theory for curves of a fixed gonality, Forum Math. Pi 9 (2021) MR 4199236.
[15]
Yoav Len, Martin Ulirsch, Dmitry Zakharov, Abelian tropical covers, Math. Proc. Camb. Philos. Soc. (2023) 1–22.
[16]
Diane Maclagan, Josephine Yu, Higher connectivity of tropicalizations, Math. Ann. (2021).
[17]
Dhruv Ranganathan, Logarithmic Gromov-Witten theory with expansions, Algebr. Geom. 9 (6) (2022) 714–761. MR 4518245.

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Published In

cover image Journal of Combinatorial Theory Series A
Journal of Combinatorial Theory Series A  Volume 206, Issue C
Aug 2024
481 pages

Publisher

Academic Press, Inc.

United States

Publication History

Published: 18 July 2024

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  1. Linkage
  2. Flow
  3. Root of divisor

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