On k-jet ampleness of line bundles on hyperelliptic surfaces

TL;DR

This paper establishes conditions under which line bundles on hyperelliptic surfaces are k-jet ample, specifically showing that (m,m) line bundles with m ≥ k+2 are k-jet ample across all types of hyperelliptic surfaces.

Contribution

It provides a general criterion for k-jet ampleness of (m,m) line bundles on hyperelliptic surfaces, extending previous results to all surface types.

Findings

Line bundles of type (m,m) with m ≥ k+2 are k-jet ample on hyperelliptic surfaces.

The result applies uniformly across all types of hyperelliptic surfaces.

Uses vanishing theorems to prove k-jet ampleness.

Abstract

We study k-jet ampleness of line bundles on hyperelliptic surfaces using vanishing theorems. Our main result states that on a hyperelliptic surface of an arbitrary type a line bundle of type (m,m) with m\geq k+2 is k-jet ample.