We suggest an effective algorithm for the first Bertini theorem in the case of the ground field of nonzero characteristic. This allows us to improve the double exponential lower bound for the degree of any system of generators of a polynomial ideal over a ground field. Bibliography: 5 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 403, 2012, pp. 172–196.
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Chistov, A.L. An effective version of the first Bertini theorem in nonzero characteristic and its applications. J Math Sci 190, 503–514 (2013). https://doi.org/10.1007/s10958-013-1267-z
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DOI: https://doi.org/10.1007/s10958-013-1267-z