Embedding theorems on hyperelliptic varieties

Abstract

In this paper, we investigate linear systems on hyperelliptic varieties. We prove analogues of well-known theorems on abelian varieties, like Lefschetz’s embedding theorem and higher k-jet embedding theorems. Syzygy or N_p-properties are also deduced for appropriate powers of ample line bundles. This is a first result on linear series, on hyperelliptic varieties.