Tropical count of curves on abelian varieties

Lars Halvard Halle; Simon Charles Florian Rose

Tropical count of curves on abelian varieties

Lars Halvard Halle, Simon Charles Florian Rose

Department of Mathematical Sciences

Abstract

We investigate the problem of counting tropical genus g curves ing-dimensional tropical abelian varieties. We do this by studyingmaps from principally polarized tropical abelian varieties into afixed abelian variety. For g = 2, 3, we prove that the tropical countmatches the count provided in [Göt98, BL99b, LS02] in the complexsetting.

Original language	English
Journal	Communications in Number Theory and Physics
Volume	11
Issue number	1
Pages (from-to)	219-248
ISSN	1931-4523
Publication status	Published - 2017

Cite this

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title = "Tropical count of curves on abelian varieties",

abstract = "We investigate the problem of counting tropical genus g curves ing-dimensional tropical abelian varieties. We do this by studyingmaps from principally polarized tropical abelian varieties into afixed abelian variety. For g = 2, 3, we prove that the tropical countmatches the count provided in [G{\"o}t98, BL99b, LS02] in the complexsetting.",

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year = "2017",

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AU - Halle, Lars Halvard

AU - Rose, Simon Charles Florian

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N2 - We investigate the problem of counting tropical genus g curves ing-dimensional tropical abelian varieties. We do this by studyingmaps from principally polarized tropical abelian varieties into afixed abelian variety. For g = 2, 3, we prove that the tropical countmatches the count provided in [Göt98, BL99b, LS02] in the complexsetting.

AB - We investigate the problem of counting tropical genus g curves ing-dimensional tropical abelian varieties. We do this by studyingmaps from principally polarized tropical abelian varieties into afixed abelian variety. For g = 2, 3, we prove that the tropical countmatches the count provided in [Göt98, BL99b, LS02] in the complexsetting.

M3 - Journal article

SN - 1931-4523

VL - 11

SP - 219

EP - 248

JO - Communications in Number Theory and Physics

JF - Communications in Number Theory and Physics

IS - 1

ER -