UC San Diego

The Kawamata-Morrison cone conjecture have attracted a lot of attention in algebraic geometry. In this thesis, the author will deal with this conjecture for Calabi-Yau 3-folds whose nef cone is polyhedral in chapter 3. In chapter 4, we will investigate the null cone and the automorphism group of Calabi-Yau 3-folds of Picard number $4$, which serves as a very good example for understanding the Kawamata-Morrison conjecture.