Communications in Number Theory and Physics

Volume 11 (2017)

Number 1

Tropical count of curves on abelian varieties

Pages: 219 – 248

DOI: http://dx.doi.org/10.4310/CNTP.2017.v11.n1.a5

Authors

Lars Halvard Halle (Department of Mathematical Sciences, University of Copenhagen, Denmark)

Simon C. F. Rose (Department of Mathematical Sciences, University of Copenhagen, Denmark)

Abstract

We investigate the problem of counting tropical genus $g$ curves in $g$-dimensional tropical abelian varieties. We do this by studying maps from principally polarized tropical abelian varieties into a fixed abelian variety. For $g = 2, 3$, we prove that the tropical count matches the count provided in [Göt98, BL99b, LS02] in the complex setting.

Full Text (PDF format)

Received 2 November 2016

Published 16 June 2017