Polar degrees and closest points in codimension two

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Martin Helmer, Bernt Ivar Utstøl Nødland

Suppose that (Formula presented.) is a toric variety of codimension two defined by an (Formula presented.) integer matrix (Formula presented.), and let (Formula presented.) be a Gale dual of (Formula presented.). In this paper, we compute the Euclidean distance degree and polar degrees of (Formula presented.) (along with other associated invariants) combinatorially working from the matrix (Formula presented.). Our approach allows for the consideration of examples that would be impractical using algebraic or geometric methods. It also yields considerably simpler computational formulas for these invariants, allowing much larger examples to be computed much more quickly than the analogous combinatorial methods using the matrix (Formula presented.) in the codimension two case.

Original languageEnglish
Article number1950095
JournalJournal of Algebra and its Applications
Issue number5
Number of pages25
Publication statusPublished - 2019

    Research areas

  • algebraic geometry, Chern–Mather class, codimension two, combinatorics, Euclidean distance degree, polar degrees, polytopes, Toric varieties

ID: 199804493