The dimensions of such sets are computed in the case of symbolic spaces. The number of entries should be minimal. Necessary and sufficient conditions upon the form germ with regular degeneracy to have such a disaggregation are found. This problem originates from recent papers of P.A. Chiappori and I. Ekeland on the mathematical economy. We prove that, under the assumptions that the multiplicities are at most 3 and the degree is high enough, these curves are irreducible and smooth away from the prescribed singularities.
C be a polynomial function.
We define global polar invariants associated to fibres of f and we describe a CW-complex model of a fibre. We show how to use affine polar curves in order to study the monodromy around atypical values of f, including the value infinity. We give a zeta-function formula for such a monodromy. In the same way, all generic set of imbedded symplectic spheres of degree I which are positively transverse to one another is symplectically isotopic to a set of complex lines. The discriminant of the set of unitary complex polynomials of degree n is the variety of polynomials having at least one double root.