Lushin, Alexey; Pochekutov, Dmitry Toric cycles in the complement to a complex curve in \(({\mathbb{C}^\times})^2\). (English) Zbl 1475.14119 Math. Nachr. 292, No. 12, 2654-2661 (2019). 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 Keywords:algebraic curve; amoeba; coamoeba; complex torus; Harnack polynomial; homological independence; Newton polygon; toric cycle PDFBibTeX XMLCite \textit{A. Lushin} and \textit{D. Pochekutov}, Math. Nachr. 292, No. 12, 2654--2661 (2019; Zbl 1475.14119) Full Text: DOI arXiv