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
APA
Vancouver
Author
Bibtex
}
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