Polynomial-time computation of the degree of a dominant morphism in zero characteristic. IV

Consider a projective algebraic variety W that is an irreducible component of the set of all common zeros of a family of homogeneous polynomials of degrees less than d in n + 1 variables in zero characteristic. Consider a dominant rational morphism from W to W′ given by homogeneous polynomials of degree d′. We suggest algorithms for constructing objects in general position related to this morphism. These algorithms are deterministic and polynomial in (dd′) ⁿ and the size of the input. This work concludes a series of four papers. Bibliography: 13 titles. Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 360, 2008, pp. 260–294.