Toric cycles in the complement to a complex curve in (C×)2

Alexey Lushin and Dmitry Pochekutov

Mathematische Nachrichten, 2019, vol. 292, issue 12, 2654-2661

Abstract: 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.

Date: 2019
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