Orders of branch points of complete diagonals for Laurent series of rational functions of two variables

D. Yu. Pochekutov

Siberian Federal University, 79 Svobodny Ave., Krasnoyarsk, 660041 Russia

Abstract: A rational function of two complex variables and all its Laurent expansions centered at an origin are considered. It is known that the complete diagonal of such an expansion is an algebraic function. The order of a branch point of the diagonal by means of the logarithmic Gauss mapping of a polar curve of the rational function is described.

Keywords: amoeba of an algebraic curve, diagonal of Laurent series, logarithmic Gauss mapping, order of a branch point, toric morphism.

UDC: 517.55

Received: 18.06.2024
Revised: 10.09.2024
Accepted: 26.09.2024

DOI: 10.26907/0021-3446-2025-9-58-69