A Numerical Approach for Computing Euler Characteristics of Affine Varieties

We develop a numerical nonlinear algebra approach for computing the Euler characteristic of an affine variety. Our approach is to relate Euler characteristics of a smooth affine variety with the number of critical points using Morse theory. In general, we stratify a variety into the union of smooth...

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Detalles Bibliográficos
Autores principales: Li, Xiaxin, Rodriguez, Jose Israel, Wang, Botong
Formato: Online Artículo Texto
Lenguaje:English
Publicado: 2020
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7340896/
http://dx.doi.org/10.1007/978-3-030-52200-1_5
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author Li, Xiaxin
Rodriguez, Jose Israel
Wang, Botong
author_facet Li, Xiaxin
Rodriguez, Jose Israel
Wang, Botong
author_sort Li, Xiaxin
collection PubMed
description We develop a numerical nonlinear algebra approach for computing the Euler characteristic of an affine variety. Our approach is to relate Euler characteristics of a smooth affine variety with the number of critical points using Morse theory. In general, we stratify a variety into the union of smooth affine varieties to obtain results on singular varieties.
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spelling pubmed-73408962020-07-08 A Numerical Approach for Computing Euler Characteristics of Affine Varieties Li, Xiaxin Rodriguez, Jose Israel Wang, Botong Mathematical Software – ICMS 2020 Article We develop a numerical nonlinear algebra approach for computing the Euler characteristic of an affine variety. Our approach is to relate Euler characteristics of a smooth affine variety with the number of critical points using Morse theory. In general, we stratify a variety into the union of smooth affine varieties to obtain results on singular varieties. 2020-06-06 /pmc/articles/PMC7340896/ http://dx.doi.org/10.1007/978-3-030-52200-1_5 Text en © Springer Nature Switzerland AG 2020 This article is made available via the PMC Open Access Subset for unrestricted research re-use and secondary analysis in any form or by any means with acknowledgement of the original source. These permissions are granted for the duration of the World Health Organization (WHO) declaration of COVID-19 as a global pandemic.
spellingShingle Article
Li, Xiaxin
Rodriguez, Jose Israel
Wang, Botong
A Numerical Approach for Computing Euler Characteristics of Affine Varieties
title A Numerical Approach for Computing Euler Characteristics of Affine Varieties
title_full A Numerical Approach for Computing Euler Characteristics of Affine Varieties
title_fullStr A Numerical Approach for Computing Euler Characteristics of Affine Varieties
title_full_unstemmed A Numerical Approach for Computing Euler Characteristics of Affine Varieties
title_short A Numerical Approach for Computing Euler Characteristics of Affine Varieties
title_sort numerical approach for computing euler characteristics of affine varieties
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7340896/
http://dx.doi.org/10.1007/978-3-030-52200-1_5
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