Garbary, Robert2015-01-092015-01-092015-01-092014-12-04http://hdl.handle.net/10012/9050In this thesis, we define a measure for how `positive' an effective line bundle is at a point on a variety, and prove that it is linear on the numerically effective subcone on a smooth, complete, toric surface.enAlgebraic GeometrySurfacesToric VarietiesDoctoral ThesisPure Mathematics