Generic polynomials over $\boldsymbol {Q}$ with two parameters for the transitive groups of degree five

Abstract

In this article, we construct generic polynomials over $\boldsymbol{Q}$ with two parameters for all transitive subgroups of the symmetric group of degree 5 by considering the action on the moduli space of the projective line with ordered five marked points. Although polynomials having such properties are already known, our device is unifying through all the cases, and in some cases we obtain polynomials with much simpler coefficients.