On k-Jet Ampleness of Line Bundles on Hyperelliptic Surfaces

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≥k+2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${m\geq k+2}$$\end{document} is k-jet ample.