Polynomial-Time Computation of the Degree of Algebraic Varieties in Zero Characteristic and Its Applications |
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Authors: | A L Chistov |
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Institution: | (1) Automation RAS, St. Petersburg Institute of Computer Science and, Russia |
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Abstract: | Let k be a ground field of zero characteristic, and let V be an algebraic variety over k given as the locus of a family of polynomials of degree less than d in n variables. In the paper, we construct algorithms that have working time that is polynomial in the size of the input and d
n and compute the following: the degree of the variety V, the dimension of V in a neighborhood of a given point, the multiplicity of a given point of V, and a representative system of smooth points with their tangent spaces on each component of V. Also, we construct an algorithm for deciding whether a given morphism between two given algebraic varieties V and V' is dominant. Bibliography: 17 titles. |
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