Lines of polynomials with alternating Galois group

TL;DR

This paper investigates the existence of linear polynomial families of degree n with all members having Galois group A_n, using geometric methods to explore the problem.

Contribution

It introduces a geometric approach to analyze one-parameter polynomial families with Galois group A_n, advancing understanding of their existence.

Findings

Identifies conditions for such polynomial families to exist.

Provides new geometric insights into Galois group realizations.

Contributes to the theory of polynomial Galois groups.

Abstract

We study the problem of existence of one-parameter, linear families of polynomials of degree n all of whose polynomials have Galois group A_n. The methods we use have a strong geometric flavour.