@article{S-On-The-Complexity-Of-Deciding-Connectedness-And-Computing-Betti-Numbers-Of-A-Complex-Algebraic-Variety,
Title = {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.},
Url = {http://www3.math.tu-berlin.de/algebra/work/conn-betti.pdf},
Url2 = {http://www.sciencedirect.com/science/article/pii/S0885064X07000556}
}