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

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Abstract

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. Bibliography: 13 titles.

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Authors and Affiliations

  1. St. Petersburg Department of the Steklov Mathematical Institute, St. Petersburg, Russia

    A. L. Chistov

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  1. A. L. Chistov
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Correspondence to A. L. Chistov.

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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 344, 2007, pp. 203–239.

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Chistov, A.L. Polynomial-time computation of the degree of a dominant morphism in zero characteristic. III. J Math Sci 147, 7234–7250 (2007). https://doi.org/10.1007/s10958-007-0540-4

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  • DOI: https://doi.org/10.1007/s10958-007-0540-4

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