The Reducibility and Dimension of Hilbert Schemes of Complex Projective Curves

Acknowledgements I want most of all to thank Joe Harris for introducing me to the beautiful geometry of algebraic curves and for guiding me through the process of writing a thesis. I could not have written this thesis without your patient and clear explanations of so many topics. You were always available to answer my questions, and I always left your office excited to continue my work. I am indebted to many members of the Harvard Mathematics Department who have taught and advised me in the past four years, especially Curtis McMullen, Michael Hopkins and Barry Mazur. Thanks also to Thomas Garrity, who introduced me to mathematical research at Williams College. Finally, thanks to my parents and my sister for encouraging me to pursue mathematics and remaining supportive whenever I encountered difficulties.

致谢 首先我要感谢乔·哈里斯，是他将我引入代数曲线的美妙几何领域，并指导我完成论文写作过程。如果没有您对众多主题耐心而清晰的讲解，我不可能完成这篇论文。您总是有求必应，解答我的问题，每次离开您的办公室，我都满怀激情地继续我的工作。 我要感谢哈佛数学系的许多成员，在过去四年里他们教导我、为我提供建议，尤其是柯蒂斯·麦克马伦、迈克尔·霍普金斯和巴里·马祖尔。还要感谢托马斯·加里蒂，是他在威廉姆斯学院引导我进入数学研究领域。 最后，感谢我的父母和姐姐，他们鼓励我追求数学，在我遇到困难时一直给予支持。