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- Title
THE GEOMETRY OF DISCOTOPES.
- Authors
GESMUNDO, F.; MERONI, C.
- Abstract
We study a class of semialgebraic convex bodies called discotopes. These are instances of zonoids, objects of interest in real algebraic geometry and random geometry. We focus on the face structure and on the boundary hypersurface of discotopes, highlighting interesting birational properties which may be investigated using tools from algebraic geometry. When a discotope is the Minkowski sum of two-dimensional discs, the Zariski closure of its set of extreme points is an irreducible hypersurface. In this case, we provide an upper bound for the degree of the hypersurface, drawing connections to the theory of classical determinantal varieties.
- Subjects
ALGEBRAIC geometry; GEOMETRY; POINT set theory; CONVEX bodies; HYPERSURFACES
- Publication
Le Matematiche, 2022, Vol 77, Issue 1, p143
- ISSN
0373-3505
- Publication type
Article
- DOI
10.4418/2022.77.1.8