caa a22 4500 605525811 CHVBK 20210128105159.0 cr unu---uuuuu 210128e20150901xx s 000 0 eng 10.1007/s10958-015-2543-x doi (NATIONALLICENCE)springer-10.1007/s10958-015-2543-x Chistov A. St.Petersburg Department of Steklov Mathematical Institute, St.Petersburg, Russia aut A Deterministic Polynomial-Time Algorithm for the First Bertini Theorem. III [Elektronische Daten] [A. Chistov] 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 linear system on W given by homogeneous polynomials of degree d′. Under the conditions of the first Bertini theorem for W and this linear system, we show how to construct an irreducible divisor in general position from the statement of this theorem. This algorithm is deterministic and polynomial in (dd′)n and the size of the input. This work concludes a three-part series of papers. Springer Science+Business Media New York, 2015 Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 209/6(2015-09-01), 1005-1019 1072-3374 209:6<1005 2015 209 10958 https://doi.org/10.1007/s10958-015-2543-x text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10958-015-2543-x text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Chistov A. St.Petersburg Department of Steklov Mathematical Institute, St.Petersburg, Russia aut NATIONALLICENCE 773 0- Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 209/6(2015-09-01), 1005-1019 1072-3374 209:6<1005 2015 209 10958 SWISSBIB 560503091