TU Berlin

Fachgebiet Algorithmische AlgebraProf. Dr. Peter Bürgisser

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Prof. Dr. Peter Bürgisser

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Technische Universität Berlin
Institut für Mathematik
Sekretariat MA 3-2
Straße des 17. Juni 136
10623 Berlin

Büro
Raum MA 317 (3. OG)
Institut für Mathematik

Kontakt

Sekretariat
Beate Nießen
Raum MA 318
Tel.: +49 (0)30 314 - 25771

eMail
peter.buergisser@offmath.tu-berlin.de

Telefon
+49 (0)30 314 - 75902
Faxgerät
+49 (0)30 314 - 25839

Sprechstunde
Während der Vorlesungszeit: Do, 15-16 Uhr.
Während der vorlesungsfreien Zeit: nach Vereinbarung.

Publikationen

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.
Link to publication Link to original publication Download Bibtex entry

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