A note on k-very ampleness of line bundles on general blow-ups of hyperelliptic surfaces

TL;DR

This paper investigates conditions under which line bundles on blow-ups of hyperelliptic surfaces at general points are k-very ample, providing numerical criteria for embedding properties.

Contribution

It introduces a new numerical condition for k-very ampleness of line bundles on blow-ups of hyperelliptic surfaces at general points.

Findings

Derived a numerical criterion for k-very ampleness

Established embedding conditions for line bundles

Analyzed blow-ups at very general points

Abstract

We study k-very ampleness of line bundles on blow-ups of hyperelliptic surfaces at r very general points. We obtain a numerical condition on the number of points for which a line bundle on the blow-up of a hyperelliptic surface at these r points gives an embedding of order k.