Toric Cycles in the Complement of a Complex Curve in $(\mathbb{C}^{\times})^2$

Alexey Lushin; Dmitry Pochekutov

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arXiv · 1707.05704

Toric Cycles in the Complement of a Complex Curve in $(\mathbb{C}^{\times})^2$

Alexey Lushin·Dmitry Pochekutov

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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.

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Alexey Lushin, Dmitry Pochekutov. 2017-07-18. Toric Cycles in the Complement of a Complex Curve in $(\mathbb{C}^{\times})^2$. https://arxiv.org/abs/1707.05704

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