Computing the Chern–Schwartz–MacPherson class of complete simplical toric varieties

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

Standard

Computing the Chern–Schwartz–MacPherson class of complete simplical toric varieties. / Helmer, Martin.

Applications of Computer Algebra: Kalamata, Greece, July 20–23 2015. Springer New York LLC, 2017. p. 207-217 (Springer Proceedings in Mathematics and Statistics, Vol. 198).

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

Harvard

Helmer, M 2017, Computing the Chern–Schwartz–MacPherson class of complete simplical toric varieties. in Applications of Computer Algebra: Kalamata, Greece, July 20–23 2015. Springer New York LLC, Springer Proceedings in Mathematics and Statistics, vol. 198, pp. 207-217, 21st International Conference on Applications of Computer Algebra, ACA 2015, Kalamata, Greece, 20/07/2015. https://doi.org/10.1007/978-3-319-56932-1_13

APA

Helmer, M. (2017). Computing the Chern–Schwartz–MacPherson class of complete simplical toric varieties. In Applications of Computer Algebra: Kalamata, Greece, July 20–23 2015 (pp. 207-217). Springer New York LLC. Springer Proceedings in Mathematics and Statistics Vol. 198 https://doi.org/10.1007/978-3-319-56932-1_13

Vancouver

Helmer M. Computing the Chern–Schwartz–MacPherson class of complete simplical toric varieties. In Applications of Computer Algebra: Kalamata, Greece, July 20–23 2015. Springer New York LLC. 2017. p. 207-217. (Springer Proceedings in Mathematics and Statistics, Vol. 198). https://doi.org/10.1007/978-3-319-56932-1_13

Author

Helmer, Martin. / Computing the Chern–Schwartz–MacPherson class of complete simplical toric varieties. Applications of Computer Algebra: Kalamata, Greece, July 20–23 2015. Springer New York LLC, 2017. pp. 207-217 (Springer Proceedings in Mathematics and Statistics, Vol. 198).

Bibtex

@inproceedings{928d3d2cdd63451bb3681d5ac201bbd8,

title = "Computing the Chern–Schwartz–MacPherson class of complete simplical toric varieties",

abstract = "Topological invariants such as characteristic classes are an important tool to aid in understanding and categorizing the structure and properties of algebraic varieties. In this note, we consider the problem of computing a particular characteristic class, the Chern–Schwartz–MacPherson class, of a complete simplicial toric variety X∑ defined by a fan ∑ from the combinatorial data contained in the fan ∑. Specifically, we give an effective combinatorial algorithm to compute the Chern–Schwartz–MacPherson class of X∑, in the Chow ring (or rational Chow ring) of X∑. This method is formulated by combining, and when necessary modifying, several known results from the literature and is implemented in Macaulay2 for test purposes.",

keywords = "Chern class, Chern–Schwartz–MacPherson class, Computational intersection theory, Computer algebra, Toric varieties",

author = "Martin Helmer",

year = "2017",

doi = "10.1007/978-3-319-56932-1_13",

language = "English",

isbn = "9783319569307",

series = "Springer Proceedings in Mathematics and Statistics",

publisher = "Springer New York LLC",

pages = "207--217",

booktitle = "Applications of Computer Algebra",

note = "21st International Conference on Applications of Computer Algebra, ACA 2015 ; Conference date: 20-07-2015 Through 23-07-2015",

}

RIS

TY - GEN

T1 - Computing the Chern–Schwartz–MacPherson class of complete simplical toric varieties

AU - Helmer, Martin

PY - 2017

Y1 - 2017

N2 - Topological invariants such as characteristic classes are an important tool to aid in understanding and categorizing the structure and properties of algebraic varieties. In this note, we consider the problem of computing a particular characteristic class, the Chern–Schwartz–MacPherson class, of a complete simplicial toric variety X∑ defined by a fan ∑ from the combinatorial data contained in the fan ∑. Specifically, we give an effective combinatorial algorithm to compute the Chern–Schwartz–MacPherson class of X∑, in the Chow ring (or rational Chow ring) of X∑. This method is formulated by combining, and when necessary modifying, several known results from the literature and is implemented in Macaulay2 for test purposes.

AB - Topological invariants such as characteristic classes are an important tool to aid in understanding and categorizing the structure and properties of algebraic varieties. In this note, we consider the problem of computing a particular characteristic class, the Chern–Schwartz–MacPherson class, of a complete simplicial toric variety X∑ defined by a fan ∑ from the combinatorial data contained in the fan ∑. Specifically, we give an effective combinatorial algorithm to compute the Chern–Schwartz–MacPherson class of X∑, in the Chow ring (or rational Chow ring) of X∑. This method is formulated by combining, and when necessary modifying, several known results from the literature and is implemented in Macaulay2 for test purposes.

KW - Chern class

KW - Chern–Schwartz–MacPherson class

KW - Computational intersection theory

KW - Computer algebra

KW - Toric varieties

UR - http://www.scopus.com/inward/record.url?scp=85028320961&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-56932-1_13

DO - 10.1007/978-3-319-56932-1_13

M3 - Article in proceedings

AN - SCOPUS:85028320961

SN - 9783319569307

T3 - Springer Proceedings in Mathematics and Statistics

SP - 207

EP - 217

BT - Applications of Computer Algebra

PB - Springer New York LLC

T2 - 21st International Conference on Applications of Computer Algebra, ACA 2015

Y2 - 20 July 2015 through 23 July 2015

ER -

ID: 183131609