TOPOLOGY OF COMPLEMENTS OF STRATA OF THE DISCRIMINANT OF POLYNOMIALS

The discriminant of the set of unitary complex polynomials of degree n is the variety of polynomials having at least one double root. For n large enough, the set of roots of a polynomial may have more complicat ed singularities. The discriminant is stratified by the varieties of p olynomials having given singularities. We study the cohomology groups of the complement of any stratum and we construct a cellular decomposi tion of the symmetric n-th power of C ''compatible'' with the stratifi cation. Using this decomposition, one can compute by hand the first co homology groups. (C) Academie des Sciences/Elsevier, Paris.