TU Berlin

Fachgebiet Algorithmische AlgebraDr. Peter Scheiblechner

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Ehemalige Mitarbeiter

Dr. Peter Scheiblechner


Lucerne University of Applied Sciences and Arts
Technology and Architecture
Technikumstr. 21
CH-6048 Horw
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Counting Irreducible Components of Complex Algebraic Varieties
Citation key BS-Counting-Irreducible-Components-Of-Complex-Algebraic-Varieties
Author Peter Bürgisser and Peter Scheiblechner
Pages 1-35
Year 2010
ISSN 1016-3328
DOI 10.1007/s00037-009-0283-3
Journal Computational Complexity
Volume 19
Number 1
Abstract We present an algorithm for counting the irreducible components of a complex algebraic variety defined by a fixed number of polynomials encoded as straight-line programs (slps). It runs in polynomial time in the Blum-Shub-Smale (BSS) model and in randomized parallel polylogarithmic time in the Turing model, both measured in the lengths and degrees of the slps. Our algorithm is obtained from an explicit version of Bertini's theorem. For its analysis we further develop a general complexity theoretic framework appropriate for algorithms in algebraic geometry.
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