Algorithms to compute the topological Euler characteristic, Chern-Schwartz-MacPherson class and Segre class of projective varieties

Research output: Contribution to journal › Journal article › Research › peer-review

Standard

Algorithms to compute the topological Euler characteristic, Chern-Schwartz-MacPherson class and Segre class of projective varieties. / Helmer, Martin.

In: Journal of Symbolic Computation, Vol. 73, 01.03.2016, p. 120-138.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Helmer, M 2016, 'Algorithms to compute the topological Euler characteristic, Chern-Schwartz-MacPherson class and Segre class of projective varieties', Journal of Symbolic Computation, vol. 73, pp. 120-138. https://doi.org/10.1016/j.jsc.2015.03.007

APA

Helmer, M. (2016). Algorithms to compute the topological Euler characteristic, Chern-Schwartz-MacPherson class and Segre class of projective varieties. Journal of Symbolic Computation, 73, 120-138. https://doi.org/10.1016/j.jsc.2015.03.007

Vancouver

Helmer M. Algorithms to compute the topological Euler characteristic, Chern-Schwartz-MacPherson class and Segre class of projective varieties. Journal of Symbolic Computation. 2016 Mar 1;73:120-138. https://doi.org/10.1016/j.jsc.2015.03.007

Author

Helmer, Martin. / Algorithms to compute the topological Euler characteristic, Chern-Schwartz-MacPherson class and Segre class of projective varieties. In: Journal of Symbolic Computation. 2016 ; Vol. 73. pp. 120-138.

Bibtex

@article{94a9b7c1a29849d6a631063d1661c326,
title = "Algorithms to compute the topological Euler characteristic, Chern-Schwartz-MacPherson class and Segre class of projective varieties",
abstract = "Let V be a closed subscheme of a projective space Pn. We give an algorithm to compute the Chern-Schwartz-MacPherson class, and the Euler characteristic of V and an algorithm to compute the Segre class of V. The algorithms can be implemented using either symbolic or numerical methods. The algorithms are based on a new method for calculating the projective degrees of a rational map defined by a homogeneous ideal. Relationships between the algorithms developed here and other existing algorithms are discussed. The algorithms are tested on several examples and are found to perform favourably compared to current algorithms for computing Chern-Schwartz-MacPherson classes, Segre classes and Euler characteristics.",
keywords = "Chern-Schwartz-MacPherson class, Computational intersection theory, Computer algebra, Euler characteristic, Segre class",
author = "Martin Helmer",
year = "2016",
month = mar,
day = "1",
doi = "10.1016/j.jsc.2015.03.007",
language = "English",
volume = "73",
pages = "120--138",
journal = "Journal of Symbolic Computation",
issn = "0747-7171",
publisher = "Academic Press",

}

RIS

TY - JOUR

T1 - Algorithms to compute the topological Euler characteristic, Chern-Schwartz-MacPherson class and Segre class of projective varieties

AU - Helmer, Martin

PY - 2016/3/1

Y1 - 2016/3/1

N2 - Let V be a closed subscheme of a projective space Pn. We give an algorithm to compute the Chern-Schwartz-MacPherson class, and the Euler characteristic of V and an algorithm to compute the Segre class of V. The algorithms can be implemented using either symbolic or numerical methods. The algorithms are based on a new method for calculating the projective degrees of a rational map defined by a homogeneous ideal. Relationships between the algorithms developed here and other existing algorithms are discussed. The algorithms are tested on several examples and are found to perform favourably compared to current algorithms for computing Chern-Schwartz-MacPherson classes, Segre classes and Euler characteristics.

AB - Let V be a closed subscheme of a projective space Pn. We give an algorithm to compute the Chern-Schwartz-MacPherson class, and the Euler characteristic of V and an algorithm to compute the Segre class of V. The algorithms can be implemented using either symbolic or numerical methods. The algorithms are based on a new method for calculating the projective degrees of a rational map defined by a homogeneous ideal. Relationships between the algorithms developed here and other existing algorithms are discussed. The algorithms are tested on several examples and are found to perform favourably compared to current algorithms for computing Chern-Schwartz-MacPherson classes, Segre classes and Euler characteristics.

KW - Chern-Schwartz-MacPherson class

KW - Computational intersection theory

KW - Computer algebra

KW - Euler characteristic

KW - Segre class

UR - http://www.scopus.com/inward/record.url?scp=84939652481&partnerID=8YFLogxK

U2 - 10.1016/j.jsc.2015.03.007

DO - 10.1016/j.jsc.2015.03.007

M3 - Journal article

AN - SCOPUS:84939652481

VL - 73

SP - 120

EP - 138

JO - Journal of Symbolic Computation

JF - Journal of Symbolic Computation

SN - 0747-7171

ER -

ID: 183131641