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.
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. III”, Representation theory, dynamical systems, combinatorial methods. Part XV, Zap. Nauchn. Sem. POMI, 344, POMI, St. Petersburg, 2007, 203–239; J. Math. Sci. (N. Y.), 147:6 (2007), 7234–7250
This publication is cited in the following 5 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. II”, J. Math. Sci. (N. Y.), 138:3 (2006), 5733–5752
Citation in format AMSBIB
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