Polar degrees and closest points in codimension two
Research output: Contribution to journal › Journal article › Research › peer-review
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.
|Journal||Journal of Algebra and its Applications|
|Number of pages||25|
|Publication status||Published - 2019|
- algebraic geometry, Chern–Mather class, codimension two, combinatorics, Euclidean distance degree, polar degrees, polytopes, Toric varieties