Correspondence theorems for tropical curves I
Abstract
In this paper, we study the deformation theory of degenerate algebraic curves on singular varieties which appear as the degenerate limit of families of varieties. For this purpose, we systematically develop a new method to calculate the obstruction cohomology class of degenerate algebraic curves. This enables us to judge whether a given degenerate curve can be deformed to a smooth curve or not in variety of situations. In this paper, we apply it to curves of genus one on degeneration of toric varieties. In particular, we obtain the necessary and sufficient condition for the realizability of tropical curves of genus one, extending various results obtained so far.
Keywords
Cite
@article{arxiv.0912.5090,
title = {Correspondence theorems for tropical curves I},
author = {Takeo Nishinou},
journal= {arXiv preprint arXiv:0912.5090},
year = {2017}
}
Comments
v2:Added references. v3:Corrected the case with higher edge weights, other modifications throughout. v4: Extensively reorganized, some parts are moved to other papers