Four Generated Rank 2 Arithmetically Cohen-Macaulay Vector Bundles on General Sextic Surfaces

In this dissertation, we compute the dimension of the moduli space, of four generated indecomposable rank 2 arithmetically Cohen-Macaulay: ACM for short) bundles on a general sextic surface. In Chapter One we introduce preliminaries and prove on a general sextic surface, every four generated indecomposable rank 2 ACM bundle belongs to one of fourteen cases. In Chapter Two we prove for each of the fourteen cases, there exists an indecomposable rank 2 ACM bundle of that case on a general sextic surface. In Chapter Three we compute for each case, the dimension of the moduli space of four generated indecomposable rank 2 ACM bundles of that case on a general sextic surface. We do the same analysis on four generated indecomposable rank 2 ACM bundles on a general quartic surface in Chapter Four