Abstract:
Consider a projective algebraic variety WW which is an irreducible component of the set of all common zeros of a family of homogeneous polynomials of degrees less than dd in n+1n+1 variables in zero characteristic.
Consider a dominant rational morphism from WW 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 dimW>dimW′. These algorithms are
deterministic and polynomial in (dd′)n and the size of the input.
Citation:
A. L. Chistov, “Polynomial-time computation of the degree of a dominant morphism in zero characteristic. II”, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part XII, Zap. Nauchn. Sem. POMI, 325, POMI, St. Petersburg, 2005, 181–224; J. Math. Sci. (N. Y.), 138:3 (2006), 5733–5752
This publication is cited in the following 6 articles:
A. L. Chistov, “A deterministic polynomial-time algorithm for the first Bertini theorem. III”, J. Math. Sci. (N. Y.), 209:6 (2015), 1005–1019
A. L. Chistov, “A deterministic polynomial-time algorithm for the first Bertini theorem. II”, J. Math. Sci. (N. Y.), 200:6 (2014), 769–784
A. L. Chistov, “A deterministic polynomial-time algorithm for the first Bertini theorem. I”, J. Math. Sci. (N. Y.), 196:2 (2014), 223–243
A. L. Chistov, “Polynomial-time algorithms for a new model of representation of algebraic varieties (in characteristic zero)”, J. Math. Sci. (N. Y.), 174:1 (2011), 71–89
A. L. Chistov, “Polynomial-time computation of the degree of a dominant morphism in zero characteristic. IV”, J. Math. Sci. (N. Y.), 158:6 (2009), 912–927
A. L. Chistov, “Polynomial-time computation of the degree of a
dominant morphism in zero characteristic. III”, J. Math. Sci. (N. Y.), 147:6 (2007), 7234–7250
Citation in format AMSBIB
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