Sabrina Pauli

During the period I was supported by the ERC grant, I wrote the paper [BMP] with Thomas Brazelton and Stephen McKean. We provide an algebraic formula for the $\mathbb{A}^1$ -degree of a map $f:\mathbb{A}^n\to \mathbb{A}^n$ with only isolated zeros in terms of the multivariate Bezoutian, which allows us to calculate the $\mathbb{A}^1$ -degree without knowing the zeros of $f$ . This is a generalization of Cazanave's result in the case $n=1$ .

The multivariate Bezoutian can also be used to calculate the local $\mathbb{A}^1$ -degee at an isolated zero yielding a formula for the local $\mathbb{A}^1$ -degree without any restrictions on the residue field (it does not need to be separable over the base).

We also impleted code in Sage that computes the $\mathbb{A}^1$ -degree and find some useful calculation rules for the $\mathbb{A}^1$ -degree.

Project related publications

Project related preprints

[BMP] Thomas Brazelton, Stephen McKean, Sabrina Pauli, Bézoutians and the $\mathbb{A}^1$ -degree. Preprint 2021. Publically available at https://services.math.duke.edu/~mckean/bezoutian.pdf

Works in progress

Return to the QUADAG members page.