Geodesic
Polynomial-time computation of the degree of a~dominant morphism in zero characteristic.~II
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part XII, Tome 325 (2005), pp. 181-224

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Consider a projective algebraic variety $W$ which 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. They generalize some algorithms from the first part of the paper to the case $\dim W>\dim W'$. These algorithms are deterministic and polynomial in $(dd')^n$ and the size of the input. 
@article{ZNSL_2005_325_a11,
     author = {A. L. Chistov},
     title = {Polynomial-time computation of the degree of a~dominant morphism in zero {characteristic.~II}},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {181--224},
     publisher = {mathdoc},
     volume = {325},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2005_325_a11/}
}
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A. L. Chistov. Polynomial-time computation of the degree of a~dominant morphism in zero characteristic.~II. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part XII, Tome 325 (2005), pp. 181-224. http://geodesic.mathdoc.fr/item/ZNSL_2005_325_a11/