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arXiv · 1703.06694

Global Euler obstruction, global Brasselet numbers and critical points

Nicolas Dutertre·Nivaldo G. Grulha Jr
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Abstract

Let $X \subset \Bbb{C}^n$ be an equidimensional complex algebraic set and let $f: X \to \mathbb{C}$ be a polynomial function. For each $c \in \Bbb{C}$, we define the global Brasselet number of $f$ at $c$, a global counterpart of the Brasselet number defined by the authors in a previous work, and the Brasselet number at infinity of $f$ at $c$. Then we establish several formulas relating these numbers to the topology of $X$ and the critical points of $f$.

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Nicolas Dutertre, Nivaldo G. Grulha Jr. 2017-03-20. Global Euler obstruction, global Brasselet numbers and critical points. https://doi.org/10.1017/prm.2019.30

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