Algebraic boundaries of convex semi-algebraic sets

DOI10.1186/s40687-015-0022-0zbMath1381.52007arXiv1405.7822OpenAlexW2098329933WikidataQ59412769 ScholiaQ59412769MaRDI QIDQ289687

Rainer Sinn

Publication date: 31 May 2016

Published in: Research in the Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1405.7822

zbMATH Keywords

algebraic boundaryconvex semi-algebraic setprojective dual variety

Mathematics Subject Classification ID

Computational aspects of higher-dimensional varieties (14Q15) Questions of classical algebraic geometry (51N35) Semialgebraic sets and related spaces (14P10) Projective techniques in algebraic geometry (14N05) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

Related Items (13)

Lifting for Simplicity: Concise Descriptions of Convex Sets ⋮ Intersection bodies of polytopes ⋮ Extreme rays of Hankel spectrahedra for ternary forms ⋮ A Lower Bound on the Positive Semidefinite Rank of Convex Bodies ⋮ Scheme-theoretic Whitney conditions ⋮ Hyperbolic secant varieties of \(M\)-curves ⋮ Volumes of Sublevel Sets of Nonnegative Forms and Complete Monotonicity ⋮ Families of faces and the normal cycle of a convex semi-algebraic set ⋮ Fiber convex bodies ⋮ The Geometry of Discotopes ⋮ Discriminants of cyclic homogeneous inequalities of three variables ⋮ Kippenhahn's Theorem for Joint Numerical Ranges and Quantum States ⋮ Generic Spectrahedral Shadows

Cites Work

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• The central curve in linear programming
• The algebraic degree of semidefinite programming
• Projective duality and homogeneous spaces
• Hyperbolic programs, and their derivative relaxations
• Determinantal representations of hyperbolic plane curves: an elementary approach
• Discriminants, resultants, and multidimensional determinants
• Multivariate Gaussians, semidefinite matrix completion, and convex algebraic geometry
• LMI Representations of Convex Semialgebraic Sets and Determinantal Representations of Algebraic Hypersurfaces: Past, Present, and Future
• On the convex hull of a space curve
• The Convex Hull of a Variety
• Exposed Faces of Semidefinitely Representable Sets
• Positive Polynomials and Projections of Spectrahedra
• Dualities in Convex Algebraic Geometry
• Semidefinite Optimization and Convex Algebraic Geometry
• Convex Analysis

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