Kov\'acs, S\'andorDeVleming, Kristin Elizabeth2018-07-312018-07-312018-07-312018DeVleming_washington_0250E_18905.pdfhttp://hdl.handle.net/1773/42454Thesis (Ph.D.)--University of Washington, 2018The main goal of this paper is to construct a compactification of the moduli space of degree $d \ge 5$ hypersurfaces in $\mathbb{P}^3$, i.e. a parameter space whose interior points correspond to (equivalence classes of) smooth hypersurfaces in $\mathbb{P}^3$ and whose boundary points correspond to degenerations of such hypersurfaces. Following a trail blazed by numerous others (see, for example, work of Koll\'ar, Shepherd-Barron, Alexeev, and Hacking), we consider a hypersurface $D$ in $\mathbb{P}^3$ as a pair $(\mathbb{P}^3, D)$ satisfying certain properties. We find a modular compactification of such pairs and use their properties to classify the pairs on the boundary to the moduli space.application/pdfen-USnonealgebraalgebraic geometrygeometryminimal model programmoduliMathematicsMathematicsThesis