Balancing conditions in global tropical geometry
Algebraic Geometry
2016-08-01 v2
Abstract
We study tropical geometry in the global setting using Berkovich's deformation retraction. We state and prove the generalized balancing conditions in this setting. Starting with a strictly semi-stable formal scheme, we calculate certain sheaves of vanishing cycles using analytic \'etale cohomology, then we interpret the tropical weights via these cycles. We obtain the balancing condition for tropical curves on the skeleton associated to the formal scheme in terms of the intersection theory on the special fiber. Our approach works over any complete discrete valuation field.
Keywords
Cite
@article{arxiv.1304.2251,
title = {Balancing conditions in global tropical geometry},
author = {Tony Yue Yu},
journal= {arXiv preprint arXiv:1304.2251},
year = {2016}
}
Comments
19 pages. I added an example for a K3 surface, revised the definition of tropical weights, and completed the bibliography