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Journal Publications
| 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. |