Bounding the number of connected components of a real algebraic set

DOI10.1007/BF02574685zbMath0743.14040OpenAlexW2042646699MaRDI QIDQ1174716

Riccardo Benedetti, François Loeser, Jean-Jacques Risler

Publication date: 25 June 1992

Published in: Discrete \& Computational Geometry (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/131154

zbMATH Keywords

number of connected componentscomplexity measureNewton polyhedra of defining equationsreal affine algebraic set

Mathematics Subject Classification ID

Toric varieties, Newton polyhedra, Okounkov bodies (14M25) Real algebraic sets (14P05)

Related Items

Qualification Conditions in Semialgebraic Programming, Random polytopes in smooth convex bodies, Polynomial bound on the local Betti numbers of a real analytic germ, Refined bounds on the number of connected components of sign conditions on a variety, A sharper estimate on the Betti numbers of sets defined by quadratic inequalities, Multi-degree bounds on the Betti numbers of real varieties and semi-algebraic sets and applications, Some speed-ups and speed limits for real algebraic geometry

Cites Work

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• Cohomologie des variétés algébriques
• Upper bounds for configurations and polytopes in \({\mathbb{R}}^ d\)
• Newton polyhedra and toroidal varieties
• Congruences modulo 16 in Hilbert's sixtieth problem
• Topological stability of smooth mappings
• Newton polyhedra and the genus of complete intersections
• Neighborhoods of Algebraic Sets
• NEWTON POLYHEDRA AND AN ALGORITHM FOR COMPUTING HODGE–DELIGNE NUMBERS
• Lower Bounds for Approximation by Nonlinear Manifolds
• Singular Points of Complex Hypersurfaces. (AM-61)
• On the Betti Numbers of Real Varieties