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On the complexity of deciding connectedness and computing Betti numbers of a complex algebraic variety
Citation key S-On-The-Complexity-Of-Deciding-Connectedness-And-Computing-Betti-Numbers-Of-A-Complex-Algebraic-Variety
Author Peter Scheiblechner
Pages 359-379
Year 2007
Journal Journal of Complexity
Volume 23
Number 3
Abstract We extend the lower bounds on the complexity of computing Betti numbers proved in [Buergisser, Cucker] to complex algebraic varieties. More precisely, we first prove that the problem of deciding connectedness of a complex affine or projective variety given as the zero set of integer polynomials is PSPACE-hard. Then we prove FPSPACE-hardness for the more general problem of computing Betti numbers of fixed order of a complex projective variety.
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