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Toric cycles in the complement to a complex curve in \(({\mathbb{C}^\times})^2\). (English) Zbl 1475.14119

Summary: The amoeba of a complex curve in the 2-dimensional complex torus is its image under the projection onto the real parts of the logarithmic coordinates. A toric cycle in the complement to a curve is a fiber of this projection over a point in the complement to the amoeba of the curve. We consider amoebas of complex algebraic curves defined by so-called Harnack polynomials. We prove that toric cycles are homologically independent in the complement to a such curve.

MSC:

14T20 Geometric aspects of tropical varieties
14T15 Combinatorial aspects of tropical varieties
32A27 Residues for several complex variables
32A60 Zero sets of holomorphic functions of several complex variables
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