A Numerical Approach for Computing Euler Characteristics of Affine Varieties

Xiaxin Li,Botong Wang,Jose Israel Rodriguez

doi:10.1007/978-3-030-52200-1_5

A Numerical Approach for Computing Euler Characteristics of Affine Varieties

Xiaxin Li, Botong Wang + Show 1 more

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https://doi.org/10.1007/978-3-030-52200-1_5

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Publication Date: Jan 1, 2020

License type: NO-CC CODE

Affiliation: University of California, San Diego, University of Wisconsin–Madison

#Affine Varieties #Number Of Critical Points + Show 8 more

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Abstract

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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