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A Numerical Approach for Computing Euler Characteristics of Affine Varieties

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (2020) 12097 LNCS 51-60
DOI: 10.1007/978-3-030-52200-1_5
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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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Li, X., Rodriguez, J. I., & Wang, B. (2020). A Numerical Approach for Computing Euler Characteristics of Affine Varieties. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 12097 LNCS, pp. 51–60). Springer. https://doi.org/10.1007/978-3-030-52200-1_5

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