A note on Galois embeddings of abelian varieties

Abstract

In this note we show that if an abelian variety possesses a Galois embedding into some projective space, then it must be isogenous to the self product of an elliptic curve. We prove moreover that the self product of an elliptic curve always has infinitely many Galois embeddings.

Some typos fixed. To appear in Manuscripta Mathematica