Mathematical Research Letters

Volume 18 (2011)

Number 4

Hodge Groups of Certain Superelliptic Jacobians II

Pages: 579 – 590



Jiangwei Xue (National Center for Theoretical Sciences, Mathematical Division, National Tsing Hua University, Third General Building, No.101, Sec 2, Kuang Fu Road, Hsinchu, Taiwan 30043, Taiwan R.O.C.)


We determine the Hodge group of certain simple factor of the Jacobian of the superelliptic curve $y^q=f(x)$, assuming that the ground field is a subfield of the complex numbers, $f(x)$ is an degree $n \geq 4$ irreducible polynomial with “large” galois group, and $q$ is a prime power coprime to $n$ and greater than $n$. The case $q<n$ was previous treated in a joint work with Yu.G. Zarhin.

Published 19 August 2011