Embedding properties of linear series on hyperelliptic varieties

TL;DR

This paper explores the embedding properties of linear series on hyperelliptic varieties, establishing analogues of classical theorems and analyzing syzygy properties for line bundles.

Contribution

It introduces new analogues of embedding theorems and syzygy properties for hyperelliptic varieties, extending classical results from abelian varieties.

Findings

Proved analogues of Lefschetz's embedding theorem for hyperelliptic varieties.

Established higher k-jet embedding theorems in this context.

Derived syzygy properties for powers of ample line bundles.

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.