AbstractWe suggest an approach to construction of algebraic hypersurfaces with given collection of singular points and polynomials with given collection of critical points. The approach is based on the Viro method of gluing polynomials and on the geometry of equisingular and equicritical strata in spaces of polynomials. As application we construct cuspidal plane curves of small degrees and real polynomials in two variables with given numbers of degenerate and non-degenerate critical points
AbstractThe Viro method is a powerful construction method of real nonsingular algebraic hypersurface...
International audienceA purely numerical approach to compact Riemann surfaces starting from plane al...
This works focus on computational aspects of the theory of singularities of plane algebraic curves. ...
AbstractWe suggest an approach to construction of algebraic hypersurfaces with given collection of s...
Abstract. A construction of algebraic surfaces based on two types of simple arrangements of lines, c...
We introduce the concept of a bipolar variety of a real algebraic hypersurface. This notion is then ...
AbstractViro's construction of real smooth hypersurfaces uses regular (also called convex or coheren...
Given a polynomial with complex coefficients, the celebrated Gauss-Lucas's theorem and Marden's theo...
We present an algorithm that computes the singular points of projective plane algebraic curves and d...
AbstractWe present an algorithm which, given a deformation with section of a reduced plane curve sin...
Abstract: New methods for computation of solutions of an algebraic equation of three varia...
We consider the smallest possible ramification. The corresponding pairs are represented by only fini...
There are 42 types of real singular points for irreducible real quintic curves and 49 types of real ...
International audienceA purely numerical approach to compact Riemann surfaces starting from plane al...
International audienceA purely numerical approach to compact Riemann surfaces starting from plane al...
AbstractThe Viro method is a powerful construction method of real nonsingular algebraic hypersurface...
International audienceA purely numerical approach to compact Riemann surfaces starting from plane al...
This works focus on computational aspects of the theory of singularities of plane algebraic curves. ...
AbstractWe suggest an approach to construction of algebraic hypersurfaces with given collection of s...
Abstract. A construction of algebraic surfaces based on two types of simple arrangements of lines, c...
We introduce the concept of a bipolar variety of a real algebraic hypersurface. This notion is then ...
AbstractViro's construction of real smooth hypersurfaces uses regular (also called convex or coheren...
Given a polynomial with complex coefficients, the celebrated Gauss-Lucas's theorem and Marden's theo...
We present an algorithm that computes the singular points of projective plane algebraic curves and d...
AbstractWe present an algorithm which, given a deformation with section of a reduced plane curve sin...
Abstract: New methods for computation of solutions of an algebraic equation of three varia...
We consider the smallest possible ramification. The corresponding pairs are represented by only fini...
There are 42 types of real singular points for irreducible real quintic curves and 49 types of real ...
International audienceA purely numerical approach to compact Riemann surfaces starting from plane al...
International audienceA purely numerical approach to compact Riemann surfaces starting from plane al...
AbstractThe Viro method is a powerful construction method of real nonsingular algebraic hypersurface...
International audienceA purely numerical approach to compact Riemann surfaces starting from plane al...
This works focus on computational aspects of the theory of singularities of plane algebraic curves. ...