This article provides a survey concerning Lefschetz fixed point formula and Lefschetz coincidence formula in the smooth and singular cases, moreover we show a Lefschetz type formula for the Coincidence number of two maps. ...

We have developed in the past several algorithms with intrinsic complexity bounds for the problem of point finding in real algebraic varieties. Our aim here is to give a comprehensive presentation of the geometrical tools ...

We introduce the concept of a bipolar variety of a real algebraic hypersurface. This notion is then used for the design and complexity estimations of a novel type of algorithms that finds algebraic sample points for the ...

For a real square-free multivariate polynomial F, we treat the general problem of finding real solutions of the equation F=0, provided that the real solution set {F=0}ℝ is compact. We allow that the equation F=0 may have ...

We construct singular varieties V-G associated to a polynomial mapping G : C-n -> Cn-1 where n >= 2. Let G : C-3 -> C-2 be a local submersion, we prove that if the homology or the intersection homology with total perversity ...

We construct singular varieties V G associated to a polynomial mapping G: ℂ n → ℂ n-1 where n ≥ 2. Let G: ℂ 3 → ℂ 2 be a local submersion, we prove that if the homology or the intersection homology with total perversity ...

Let V ⊂ double-struck Pn(double-struck F¯q) be a complete intersection defined over a finite field double-struck Fq of dimension r and singular locus of dimension at most s, and let π :V → double-struck Ps+1 (double-struck ...

We give a description of the tropical Severi variety of univariate polynomials of degree n having two double roots. We show that, as a set, it is given as the union of three explicit types of cones of maximal dimension n ...