On the complexity of deciding connectedness and computing Betti numbers of a complex algebraic variety

DOI10.1016/j.jco.2007.03.008zbMath1127.68038OpenAlexW2141062816MaRDI QIDQ2371309

Peter Scheiblechner

Publication date: 4 July 2007

Published in: Journal of Complexity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jco.2007.03.008

zbMATH Keywords

connected componentslower boundsBetti numbersPSPACE

Mathematics Subject Classification ID

Analysis of algorithms and problem complexity (68Q25) Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.) (68Q17) Effectivity, complexity and computational aspects of algebraic geometry (14Q20)

Related Items (7)

On a generalization of Stickelberger's theorem ⋮ Castelnuovo-Mumford regularity and computing the de Rham cohomology of smooth projective varieties ⋮ Computation of Darboux polynomials and rational first integrals with bounded degree in polynomial time ⋮ A complex analogue of Toda's theorem ⋮ Computing the homology of real projective sets ⋮ Effective de Rham cohomology — The general case ⋮ On the complexity of counting components of algebraic varieties

Cites Work

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• The complexity of semilinear problems in succinct representation
• Computing the first few Betti numbers of semi-algebraic sets in single exponential time
• Counting complexity classes for numeric computations. II: Algebraic and semialgebraic sets
• Polynomial Space Counting Problems
• Filtrations on the homology of algebraic varieties
• Counting Complexity Classes for Numeric Computations I: Semilinear Sets

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