3 papers
math.AG2026
Osculating Geometry and Higher-Order Distance Loci
Sandra Di Rocco, Kemal Rose, Luca Sodomaco
We discuss the problem of optimizing the distance function from a given point, subject to polynomial constraints. A key algebraic invariant that governs its complexity is the Eucli…
math.AG2025
On the minimal algebraic complexity of the rank-one approximation problem for general inner products
Khazhgali Kozhasov, Alan Muniz, Yang Qi +1
We study the algebraic complexity of Euclidean distance minimization from a generic tensor to a variety of rank-one tensors. The Euclidean Distance (ED) degree of the Segre-Verones…
math.AG2024
Conditional Euclidean distance optimization via relative tangency
Sandra Di Rocco, Lukas Gustafsson, Luca Sodomaco
We introduce a theory of relative tangency for projective algebraic varieties. The dual variety of a variety relative to a subvariety is the set of hyperplanes t…