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.

I: Journal of Algebra and its Applications, Bind 18, Nr. 5, 1950095, 2019.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Helmer, M & Nødland, BIU 2019, 'Polar degrees and closest points in codimension two', Journal of Algebra and its Applications, bind 18, nr. 5, 1950095. https://doi.org/10.1142/S0219498819500956

APA

Helmer, M., & Nødland, B. I. U. (2019). Polar degrees and closest points in codimension two. Journal of Algebra and its Applications, 18(5), [1950095]. https://doi.org/10.1142/S0219498819500956

Vancouver

Helmer M, Nødland BIU. Polar degrees and closest points in codimension two. Journal of Algebra and its Applications. 2019;18(5). 1950095. https://doi.org/10.1142/S0219498819500956

Author

Helmer, Martin ; Nødland, Bernt Ivar Utstøl. / Polar degrees and closest points in codimension two. I: Journal of Algebra and its Applications. 2019 ; Bind 18, Nr. 5.

Bibtex

@article{1d6dd94945ed4fb2b946aeef7bb83182,
title = "Polar degrees and closest points in codimension two",
abstract = "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.",
keywords = "algebraic geometry, Chern–Mather class, codimension two, combinatorics, Euclidean distance degree, polar degrees, polytopes, Toric varieties",
author = "Martin Helmer and N{\o}dland, {Bernt Ivar Utst{\o}l}",
year = "2019",
doi = "10.1142/S0219498819500956",
language = "English",
volume = "18",
journal = "Journal of Algebra and its Applications",
issn = "0219-4988",
publisher = "World Scientific Publishing Co. Pte. Ltd.",
number = "5",

}

RIS

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