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.
Halle, L.H., Rose, S.C.F. (2017). Tropical count of curves on abelian varieties. COMMUNICATIONS IN NUMBER THEORY AND PHYSICS, 11(1), 219-248 [10.4310/CNTP.2017.v11.n1.a5].
Tropical count of curves on abelian varieties
Halle, Lars Halvard;
2017
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.File in questo prodotto:
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