Toric Cycles in the Complement of a Complex Curve in $(\mathbb{C}^{\times})^2$
Algebraic Geometry
2017-07-19 v1 Complex Variables
Abstract
The amoeba of a complex curve in the 2-dimensional complex torus is its image under the projection onto the real subspace in the logarithmic scale. The complement to an amoeba is a disjoint union of connected components that are open and convex. A toric cycle is a 2-cycle in the complement to a curve associated with a component of the complement to an amoeba. We prove homological independence of toric cycles in the complement to a complex algebraic curve with amoeba of maximal area.
Keywords
Cite
@article{arxiv.1707.05704,
title = {Toric Cycles in the Complement of a Complex Curve in $(\mathbb{C}^{\times})^2$},
author = {Alexey Lushin and Dmitry Pochekutov},
journal= {arXiv preprint arXiv:1707.05704},
year = {2017}
}
Comments
9 pages, 4 figures, 1 table