Lifting tropical self intersections
Algebraic Geometry
2019-05-02 v2 Combinatorics
Abstract
We study the tropicalization of intersections of plane curves, under the assumption that they have the same tropicalization. We show that the set of tropical divisors that arise in this manner is a pure dimensional balanced polyhedral complex and compute its dimension. When the genus is at most 1, we show that all the tropical divisors that move in the expected dimension are realizable. As part of the proof, we introduce a combinatorial tool for explicitly constructing large families of realizable tropical divisors.
Cite
@article{arxiv.1806.01334,
title = {Lifting tropical self intersections},
author = {Yoav Len and Matthew Satriano},
journal= {arXiv preprint arXiv:1806.01334},
year = {2019}
}
Comments
17 pages, 6 figures. Major revisions from previous version