Essential dimension relative to branched covers of degree at most n

Benson Farb; Jesse Wolfson

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arXiv · 2510.22786

Essential dimension relative to branched covers of degree at most n

Benson Farb·Jesse Wolfson

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Abstract

We prove for various finite groups $G$ and integers $n\geq 1$ that there are families of equations with Galois group $G$ that cannot be simplified to a one-parameter family even after adjoining a root of a polynomial of degree at most $n$. In more geometric language, there are $G$-varieties $X$ with the following property: for any $G$-equivariant branched cover $\widetilde{X}\to X$ of degree $\leq n$, there is no dominant rational $G$-map $\widetilde{X}\dashrightarrow C$ to any $G$-curve $C$. The method of proof is new, and applies in cases where previous methods do not.

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BibTeX RIS

Benson Farb, Jesse Wolfson. 2025-10-26. Essential dimension relative to branched covers of degree at most n. https://arxiv.org/abs/2510.22786

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