Generators of Fat Point Ideals on the Projective Plane

ere have been many people who have had more faith in my abilities than I, and while their expectations have occasionally made me uncomfortable, they have also been instrumental in bringing me to this point. The following is therefore just a partial list of people to whom I am thankful for their help in preparing this dissertation. I would like to express my most sincere gratitude to Brian Harbourne for sharing with me the beauty of algebraic geometry, for his constant guidance and patience as I struggled with new ideas, and for the enormous amount of time and attention he has given me over the last several years. The breadth of his knowledge in the eld of mathematics never ceases to astound me, and his willingness to explain his thoughts has greatly increased my understanding of a variety (no pun intended) of topics. More than once during my years of graduate school, Roger Wiegand's casual assumption of my success has helped bring about that success. The commutative algebra I learned