Geodesic
Polynomial-time computation of the degree of a dominant morphism in characteristic zero. I
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part X, Tome 307 (2004), pp. 189-235 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

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 over a field of zero characteristic. We show how to compute the degree of a dominant rational morphism from $W$ to $W'$ with $\dim W=\dim W'$. The morphism is given by homogeneous polynomials of degree $d'$. This algorithm is deterministic and polynomial in $(dd')^n$ and the size of input. 
@article{ZNSL_2004_307_a6,
     author = {A. L. Chistov},
     title = {Polynomial-time computation of the degree of a~dominant morphism in characteristic {zero.~I}},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {189--235},
     year = {2004},
     volume = {307},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2004_307_a6/}
}
TY  - JOUR
AU  - A. L. Chistov
TI  - Polynomial-time computation of the degree of a dominant morphism in characteristic zero. I
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2004
SP  - 189
EP  - 235
VL  - 307
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2004_307_a6/
LA  - ru
ID  - ZNSL_2004_307_a6
ER  - 
%0 Journal Article
%A A. L. Chistov
%T Polynomial-time computation of the degree of a dominant morphism in characteristic zero. I
%J Zapiski Nauchnykh Seminarov POMI
%D 2004
%P 189-235
%V 307
%U http://geodesic.mathdoc.fr/item/ZNSL_2004_307_a6/
%G ru
%F ZNSL_2004_307_a6
A. L. Chistov. Polynomial-time computation of the degree of a dominant morphism in characteristic zero. I. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part X, Tome 307 (2004), pp. 189-235. http://geodesic.mathdoc.fr/item/ZNSL_2004_307_a6/

[1] D. Mamford, Algebraicheskaya geometriya I. Kompleksnye proektivnye mnogoobraziya, Mir, M., 1979 | MR

[2] R. Khartskhorn, Algebraicheskaya geometriya, Mir, M., 1981 | MR | Zbl

[3] V. Khodzh, D. Pido, Metody algebraicheskoi geometrii, T. 1, IIL, M., 1954

[4] A. L. Chistov, “Algoritm polinomialnoi slozhnosti dlya razlozheniya mnogochlenov na neprivodimye mnozhiteli i nakhozhdenie komponent mnogoobraziya v subeksponentsialnoe vremya”, Zap. nauchn. semin. LOMI, 137, 1984, 124–188 | MR | Zbl

[5] A. L. Chistov, “Vychislenie stepenei algebraicheskikh mnogoobrazii nad polem nulevoi kharakteristiki za polinomialnoe vremya i ego prilozheniya”, Zap. nauchn. semin. POMI, 258, 1999, 7–59 | MR | Zbl

[6] A. L. Chistov, “Silnaya versiya osnovnogo razreshayuschego algoritma dlya ekzistentsionalnoi teorii pervogo poryadka veschestvenno zamknutykh polei”, Zap. nauchn. semin. POMI, 256, 1999, 168–211 | MR | Zbl

[7] A. L. Chistov, “Monodromiya i kriterii neprivodimosti s algoritmicheskimi prilozheniyami v nulevoi kharakteristike”, Zap. nauchn. semin. POMI, 292, 2002, 130–152 | MR | Zbl

[8] J. Bochnak, M. Coste, M.-F. Roy, Géométrie Algébrique Réelle, Springer-Verlag, Berlin–Heidelberg–New York, 1987 | MR | Zbl

[9] A. L. Chistov, “Polynomial complexity of the Newton–Puiseux algorithm”, Lect. Notes Comput. Sci., 233, 1986, 247–255 | MR | Zbl

[10] A. L. Chistov, “Polynomial-time computation of the dimension of algebraic varieties in zero-characteristic”, J. Symbolic Comput., 22:1 (1996), 1–25 | DOI | MR | Zbl

[11] A. L. Chistov, “Polynomial-time computation of the dimensions of components of algebraic varieties in zero-characteristic”, J. Pure Appl. Algebra, 117–118 (1997), 145–175 | DOI | MR | Zbl