Desingularizations of some Weighted Projective Planes

In this paper we discuss the desingularization algorithm for a toric surface. In particular, we construct an iterable method of determining the Hirzebruch-Jung continued fraction decomposition. These results are then applied to weighted projective planes with at least one tivial weight, $\mathbb{P}(1,m,n)$. The paper concludes with the development of a computer program that computes this continued fraction decomposition.