Abstract
The first part of this thesis deals with cuspidal curves on Hirzebruch surfaces. Bounds are given on the number and type of cusps on cuspidal curves, and rational cuspidal curves are constructed using birational transformations.
The second part of this thesis deals with Segre classes of closed subschemes of smooth projective toric varieties. An algorithm for computing Segre classes of closed subschemes of projective spaces is generalized to an algorithm for computing Segre classes of closed subschemes of smooth projective toric varieties.