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Algebraic Distance Optimization in Polyhedral Norms
Eliana Duarte, Nidhi Kaihnsa, Julia Lindberg +2
We consider the distance minimization problem to a real algebraic variety $X \subseteq \RR^n$ when the metric is induced by a polyhedral norm. Each point in the variety has a Voron…
96120: The degree of the linear orbit of a cubic surface
Laura Brustenga i Moncusí, Sascha Timme, Madeleine Weinstein
The projective linear group \(\pgl(\comp,4)\) acts on cubic surfaces, considered as points of . We compute the degree of the -dimensional projecti…
The bottleneck degree of algebraic varieties
Sandra Di Rocco, David Eklund, Madeleine Weinstein
A bottleneck of a smooth algebraic variety is a pair of distinct points such that the Euclidean normal spaces at and contain the line…
Voronoi Cells of Varieties
Diego Cifuentes, Kristian Ranestad, Bernd Sturmfels +1
Every real algebraic variety determines a Voronoi decomposition of its ambient Euclidean space. Each Voronoi cell is a convex semialgebraic set in the normal space of the variety a…
Offset Hypersurfaces and Persistent Homology of Algebraic Varieties
Emil Horobet, Madeleine Weinstein
In this paper, we study the persistent homology of the offset filtration of algebraic varieties. We prove the algebraicity of two quantities central to the computation of persisten…
Learning Algebraic Varieties from Samples
Paul Breiding, Sara Kalisnik Verovsek, Bernd Sturmfels +1
We seek to determine a real algebraic variety from a fixed finite subset of points. Existing methods are studied and new methods are developed. Our focus lies on aspects of topolog…