Formulas for the A1-degree

by Sabrina Pauli (Universität Duisburg-Essen)

Thursday 25 Mar 2021, 12:30 → 14:30 Europe/Moscow

818-1526-4739 (Zoom)

Morel´s $\mathbb{A}^1$-degree is a very important tool in $\mathbb{A}^1$-enumerative geometry and one wishes to have nice algebraic formulas for it. One way to compute it is to express it as a sum of local degrees for which there exist formulas whenever the residue fields are separable field extensions over the ground field. Cazanave provides a global formula for the $\mathbb{A}^1$-degree of an endomorphism of $\mathbb{P}^1$ given by the so called Bezoutian. In my talk I will show how a multivariate version of the Bezoutian can be used to compute the $\mathbb{A}^1$-degree generalising Cazanave´s result and removing the assumptions on the residue fields.

This is joint work with Thomas Brazelton and Stephen McKean.

Notes from the talk Video