On metric graphs with prescribed gonality

Filip Cools, Jan Draisma

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Uittreksel

We prove that in the moduli space of genus-g metric graphs the locus of graphs with gonality at most d has the classical dimension min⁡{3g−3,2g+2d−5}. This follows from a careful parameter count to establish the upper bound and a construction of sufficiently many graphs with gonality at most d to establish the lower bound. Here, gonality is the minimal degree of a non-degenerate harmonic map to a tree that satisfies the Riemann–Hurwitz condition everywhere. Along the way, we establish a convenient combinatorial datum capturing such harmonic maps to trees.

TaalEngels
Pagina's1-21
Aantal pagina's21
TijdschriftJournal of Combinatorial Theory. Series A
Volume156
DOI's
StatusGepubliceerd - 1 mei 2018

Vingerafdruk

Gonality
Metric Graphs
Harmonic Maps
Graph in graph theory
Moduli Space
Locus
Genus
Count
Lower bound
Upper bound

Trefwoorden

    Citeer dit

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    abstract = "We prove that in the moduli space of genus-g metric graphs the locus of graphs with gonality at most d has the classical dimension min⁡{3g−3,2g+2d−5}. This follows from a careful parameter count to establish the upper bound and a construction of sufficiently many graphs with gonality at most d to establish the lower bound. Here, gonality is the minimal degree of a non-degenerate harmonic map to a tree that satisfies the Riemann–Hurwitz condition everywhere. Along the way, we establish a convenient combinatorial datum capturing such harmonic maps to trees.",
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    On metric graphs with prescribed gonality. / Cools, Filip; Draisma, Jan.

    In: Journal of Combinatorial Theory. Series A, Vol. 156, 01.05.2018, blz. 1-21.

    Onderzoeksoutput: Bijdrage aan tijdschriftTijdschriftartikelAcademicpeer review

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    KW - Brill–Noether theory

    KW - Gonality

    KW - Metric graphs

    KW - Tropical geometry

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