References & Citations
Mathematics > Algebraic Geometry
Title: Euclidean distance degree of complete intersections via Newton polytopes
(Submitted on 26 Apr 2024 (v1), last revised 2 May 2024 (this version, v2))
Abstract: In this note, we consider a complete intersection $X=\{x\in \mathbb{R}^n : f_1(x)= \ldots = f_m(x)=0\}, n>m$ and study its Euclidean distance degree in terms of the mixed volume of the Newton polytopes. We show that if the Newton polytopes of $f_j,j=1,\ldots, m$ contain the origin then when these polynomials are generic with respect to their Newton polytopes, the Euclidean distance degree of $X$ can be computed in terms of the mixed volume of Newton polytopes associated to $f_j$. This is a generalization for the result by P. Breiding, F. Sottile and J. Woodcock in case $m=1$.
Submission history
From: Tat Thang Nguyen [view email][v1] Fri, 26 Apr 2024 08:17:36 GMT (12kb)
[v2] Thu, 2 May 2024 04:00:19 GMT (12kb)
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