Hodge Groups of certain Superelliptic Jacobians II

Abstract

Let K be a field of characteristic zero, f(x) be a polynomial with coefficients in K and without multiple roots. We consider the superelliptic curve C_{f,q} defined by y^q=f(x), where q=p^r is a power of a prime p. We determine the Hodge group of the simple factors of the Jacobian of C_{f,q}.

11 pages. This paper is a natural extension of previously published paper "Hodge groups of certain superelliptic Jacobians. Math. Res. Lett. 17 (2010), no. 2, 371-388" joint by Yu.G. Zarhin and X