An algorithm to compute certain euler characteristics and chern-schwartz-macpherson classes

Martin Helmer

doi:10.1145/2631948.2631972

An algorithm to compute certain euler characteristics and chern-schwartz-macpherson classes

Martin Helmer^*

^*Corresponding author af dette arbejde

Publikation: Bidrag til bog/antologi/rapport › Konferencebidrag i proceedings › Forskning › peer review

Abstract

Let V be a possibly singular scheme-theoretic global complete intersection subscheme of Pn and assume that V can be written as the intersection of j hypersurfaces such that the intersection of j -1 of the hypersurfaces is smooth (scheme theoretically). Using a result of Fullwood [5] we develop a probabilistic algorithm to compute the Chern-Schwartz-MacPherson class (cSM) and Euler characteristic of V . This algorithm complements existing algorithms by providing performance improvements in the computation of the cSM class and Euler characteristic for schemes having the special structure described above.

Originalsprog	Engelsk
Titel	Proceedings of the 2014 Symposium on Symbolic-Numeric Computation, SNC 2014
Antal sider	2
Forlag	Association for Computing Machinery, Inc.
Publikationsdato	2014
Sider	130-131
ISBN (Trykt)	9781450329637
DOI	https://doi.org/10.1145/2631948.2631972
Status	Udgivet - 2014
Udgivet eksternt	Ja
Begivenhed	2014 Symposium on Symbolic-Numeric Computation, SNC 2014 - Shanghai, Kina Varighed: 28 jul. 2014 → 31 jul. 2014

Konference

Konference	2014 Symposium on Symbolic-Numeric Computation, SNC 2014
Land/Område	Kina
By	Shanghai
Periode	28/07/2014 → 31/07/2014
Sponsor	Academy of Mathematics and Systems Science, East China Normal University, et al, National Basic Research Program of China, National Natural Science Foundation of China, Ontario Research Centre for Computer Algebra

Adgang til dokumentet

10.1145/2631948.2631972

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Link to publication in Scopus

Citationsformater

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abstract = "Let V be a possibly singular scheme-theoretic global complete intersection subscheme of Pn and assume that V can be written as the intersection of j hypersurfaces such that the intersection of j -1 of the hypersurfaces is smooth (scheme theoretically). Using a result of Fullwood [5] we develop a probabilistic algorithm to compute the Chern-Schwartz-MacPherson class (cSM) and Euler characteristic of V . This algorithm complements existing algorithms by providing performance improvements in the computation of the cSM class and Euler characteristic for schemes having the special structure described above.",

keywords = "Chern-Schwartz-MacPherson class, Computational intersection theory, Computer algebra, Euler characteristic, Segre class",

author = "Martin Helmer",

year = "2014",

doi = "10.1145/2631948.2631972",

language = "English",

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pages = "130--131",

booktitle = "Proceedings of the 2014 Symposium on Symbolic-Numeric Computation, SNC 2014",

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AB - Let V be a possibly singular scheme-theoretic global complete intersection subscheme of Pn and assume that V can be written as the intersection of j hypersurfaces such that the intersection of j -1 of the hypersurfaces is smooth (scheme theoretically). Using a result of Fullwood [5] we develop a probabilistic algorithm to compute the Chern-Schwartz-MacPherson class (cSM) and Euler characteristic of V . This algorithm complements existing algorithms by providing performance improvements in the computation of the cSM class and Euler characteristic for schemes having the special structure described above.

KW - Chern-Schwartz-MacPherson class

KW - Computational intersection theory

KW - Computer algebra

KW - Euler characteristic

KW - Segre class

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BT - Proceedings of the 2014 Symposium on Symbolic-Numeric Computation, SNC 2014

PB - Association for Computing Machinery, Inc.

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Y2 - 28 July 2014 through 31 July 2014

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