Rational Cuspidal Curves

It is the product of my playing with beautiful geometric objects called rational cuspidal curves over the past two years. I would like to thank everyone who has contributed to this thesis. I owe so much to everyone who has ever taught me mathematics. Thank you for inspiring me and for providing me with the skills necessary to complete this thesis. To my friends and fellow students at Abel, thank you for sharing joy, hopes, dreams, disappointments, nervousness and cakes. I could not have done this without you. I would also like to thank everyone in the Algebra group at the University of Oslo for including me in their work and social events. In particular, I am very grateful to Professor Kristian Ranestad and Ph.D. student Heidi Mork for their important contributions concerning Cre-mona transformations and projections. To my friends and family, thank you for being there for me. Especially, I would like to thank my husband Kjartan Moe, who has driven 100km every day to bring in the money, who patiently has been playing Bach and Civilization while I have been playing with curves, and who has saved me from mathematical monsters more than once. Finally, I would like to thank Professor Ragni Piene for her excellent supervision and guidance. Thank you for introducing me to algebraic geometry and rational cuspidal curves, and thank you for two wonderful, unforgettable, playful and slightly insane years.