On degeneration of \(M\)-varieties (Q1358490)

To obtain a real algebraic variety with prescribed topological properties, one usually constructs a variation of a special singular variety. Also we can regard this variation as a degeneration of a real algebraic variety. Some general properties of these degenerations are proved in Math. USSR, Izv. 27, 115-140 (1986); translation from Izv. Akad. Nauk SSSR, Ser. Mat. 49, No. 4, 798-827 (1985; Zbl 0586.14022) by \textit{V. A. Krasnov}. In this paper we deal with degenerations of \(M\)-varieties and prove an inequality similar to the Harnack-Thom inequalities for mappings. Note that the application of the general Harnack-Thom inequalities for mappings [see Math. USSR, Izv. 22, 247-275 (1984); translation from Izv. Akad. Nauk SSSR, Ser. Mat. 47, No. 2, 268-297 (1983; Zbl 0537.14035)], in our situation yields inequalities that are weaker than the inequality that we prove here.