Non-isogenous superelliptic jacobians

Abstract

In his previous papers (J. reine angew. Math. 544 (2002), 91--110; math.AG/0103203) the author introduced a certain explicit construction of superelliptic jacobians, whose endomorphism ring is the ring of integers in the $p$th cyclotomic field. (Here $p$ is an odd prime.) In the present paper we discuss when these jacobians are mutually non-isogenous. (The case of hyperelliptic jacobians was treated in author's e-print math.NT/0301173 .)