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Second St.Petersburg Days of Logic and Computability
August 24-26, 2003
Petersburg Department of Steklov Institute of Mathematics
St. Petersburg, Russia

Organizers
Sergei ADIAN (Russia), Sergei ARTEMOV (Russia/USA), Nikolai KOSSOVSKI (Russia), Maurice MARGENSTERN (France), Grigori MINTS (USA), Yuri MATIYASEVICH (Russia), the chairman, Nikolai NAGORNY (Russia), Vladimir OREVKOV (Russia), Anatol SLISSENKO (France)

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Application of Monodromy to Constructing Linear Sections in General Position of an Algebraic Variety
by
Alexander L. Chistov
St. Petersburg Institute for Informatics and Automation of the Academy of Sciences of Russia

Consider a projective algebraic variety V which is the set of all common zeroes of homogeneous polynomials of degrees less than d in n+1 variables in zero-characteristic. We suggest an algorithm to decide whether two (or more) given points of V belong to the same irreducible component of V. Besides that we show how to construct for each s < n an (s+1)-dimensional plane in the projective space such that the intersection of every irreducible component of dimension n-s of V with the constructed plane is transversal and is an irreducible curve. These algorithms are deterministic and polynomial in dn and the size of input.

Date received: March 15, 2003

Copyright © 2003 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Mathematical Conference Abstracts. Document # cajy-10.