Galois groups of Mori trinomials and hyperelliptic curves with big monodromy

TL;DR

This paper computes Galois groups of specific Mori polynomials and investigates the monodromy of hyperelliptic Jacobians, advancing understanding of their algebraic and geometric properties.

Contribution

It provides explicit Galois group calculations for Mori trinomials and analyzes the monodromy of associated hyperelliptic Jacobians, revealing new structural insights.

Findings

Determined Galois groups for a class of Mori polynomials.

Analyzed monodromy representations of hyperelliptic Jacobians.

Established connections between polynomial Galois groups and Jacobian monodromy.

Abstract

We compute the Galois groups for a certain class of polynomials over the the field of rational numbers that was introduced by S. Mori and study the monodromy of corresponding hyperelliptic jacobians.