Descriptor: "Primary: 52A99, 14P05, 14P10, Secondary: 14N05, 14Q30" - Searchworks@Jio Institute Digital Library Search Results

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Author: Plaumann, Daniel, Sinn, Rainer, and Wesner, Jannik Lennart
Subjects: Mathematics - Algebraic Geometry, Primary: 52A99, 14P05, 14P10, Secondary: 14N05, 14Q30
Abstract: We study families of faces for convex semi-algebraic sets via the normal cycle which is a semi-algebraic set similar to the conormal variety in projective duality theory. We propose a convex algebraic notion of a "patch" -- a term recently coined by Ciripoi, Kaihnsa, L\"ohne, and Sturmfels as a tool for approximating the convex hull of a semi-algebraic set. We discuss geometric consequences, both for the semi-algebraic and convex geometry of the families of faces, as well as variations of our definition and their consequences., Comment: 22 pages
Published: 2021

Author: Daniel Plaumann, Rainer Sinn, and Jannik Lennart Wesner
Subjects: Mathematics - Algebraic Geometry, Primary: 52A99, 14P05, 14P10, Secondary: 14N05, 14Q30, Algebra and Number Theory, FOS: Mathematics, Geometry and Topology, Families of faces, Normal cycle, Algebraic Geometry (math.AG), Semi-algebraic sets, Convex sets
Abstract: We study families of faces for convex semi-algebraic sets via the normal cycle which is a semi-algebraic set similar to the conormal variety in projective duality theory. We propose a convex algebraic notion of a "patch" -- a term recently coined by Ciripoi, Kaihnsa, L\"ohne, and Sturmfels as a tool for approximating the convex hull of a semi-algebraic set. We discuss geometric consequences, both for the semi-algebraic and convex geometry of the families of faces, as well as variations of our definition and their consequences., Comment: 22 pages
Published: 2022

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