Generation of k-jets on toric varieties

Abstract.

The notion of a k-convex $\Delta$-support function for a toric variety $X(\Delta)$ is introduced. A criterion for a line bundle L to generate k-jets on X is given in terms of the k-convexity of the $\Delta$-support function $\psi_L$. Equivalently L is proved to be k-jet ample if and only if the restriction to each invariant curve has degree at least k.