Polar degrees and closest points in codimension two
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Polar degrees and closest points in codimension two. / Helmer, Martin; Nødland, Bernt Ivar Utstøl.
In: Journal of Algebra and its Applications, Vol. 18, No. 5, 1950095, 2019.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - Polar degrees and closest points in codimension two
AU - Helmer, Martin
AU - Nødland, Bernt Ivar Utstøl
PY - 2019
Y1 - 2019
N2 - 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.
AB - 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.
KW - algebraic geometry
KW - Chern–Mather class
KW - codimension two
KW - combinatorics
KW - Euclidean distance degree
KW - polar degrees
KW - polytopes
KW - Toric varieties
UR - http://www.scopus.com/inward/record.url?scp=85048273953&partnerID=8YFLogxK
U2 - 10.1142/S0219498819500956
DO - 10.1142/S0219498819500956
M3 - Journal article
AN - SCOPUS:85048273953
VL - 18
JO - Journal of Algebra and its Applications
JF - Journal of Algebra and its Applications
SN - 0219-4988
IS - 5
M1 - 1950095
ER -
ID: 199804493