being the number of coefficients in a generic homogenous polynomial of degree d in n + 1 variables. One associates with it the universal hypersurface Î“ âŠ‚ P Ã— P = {(p, x) | p(x) = 0}, which is aâ€¦ (More)

The Harnack bound on the number of real components of a plane real algebraic curve has a natural local version which states that the number of closed real components obtained by a perturbation of aâ€¦ (More)

We apply the Murasugi-Tristram inequality to real algebraic curves of odd degree in RP with a deep nest, i.e. a nest of the depth kâˆ’1 where 2k+1 is the degree. For such curves, the ingredients of theâ€¦ (More)

being the number of coefficients in a generic homogenous polynomial of degree d in n + 1 variables. One associates with it the universal hypersurface Î“ âŠ‚ P Ã— P = {(p, x) | p(x) = 0}, which is aâ€¦ (More)

It is shown that two braids represent transversally isotopic links if and only if one can pass from one braid to another by conjugations in braid groups, positive Markov moves, and their inverses.â€¦ (More)

We discuss the principle tools and results and state a few open problems concerning the classification and topology of plane sextics and trigonal curves in ruled surfaces.