Complexity of Counting Components of Algebraic Varieties
Irreducible and Connected Components, Betti Numbers
(Sprache: Englisch)
Complexity theory aims at the understanding of the inherent hardness of computational problems. Thisbook studies the complexity of the most basic counting problems in algebraic geometry within analgebraic framework of computation.The author gives an...
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Complexity theory aims at the understanding of the inherent hardness of computational problems. Thisbook studies the complexity of the most basic counting problems in algebraic geometry within analgebraic framework of computation.The author gives an efficient parallel method for the two problems of counting the connected andirreducible components of complex algebraic varieties. On the other hand, it is shown that decidingconnectedness of varieties is PSPACE-hard. This result is also extend to higher Betti numbers.Furthermore, the problem of counting irreducible components for a fixed number of equationsis reduced to a fixed number of variables. The consequences are a polynomial time algorithmin the BSS-model, and a randomised parallel polylogarithmic time algolrithm in the Turing model.The book is intended for mathematicians interested in computational complexity, and for computerscientists interested in algebraic geometry. The required prerequisites are completely presented, sothe text should be accessable to graduate students.
Autoren-Porträt von Peter Scheiblechner
Scheiblechner, PeterPeter Scheiblechner, Dr.rer.nat.: Study of Mathematics and Physics in Marburg and Freiburg i.Br, Germany. Consultant and Software-Developer SAP and SmallTalkin Freiburg i.Br. Doctorate under supervision of Prof. Bürgisser in Paderborn.
Bibliographische Angaben
- Autor: Peter Scheiblechner
- 2008, 160 Seiten, Maße: 15 x 22 cm, Kartoniert (TB), Englisch
- Verlag: VDM Verlag Dr. Müller e.K.
- ISBN-10: 3836498448
- ISBN-13: 9783836498449
Sprache:
Englisch
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