Weighted projective degenerations of $\mathbb{P}^{n}$

Abstract

We study weighted projective klt $\mathbb{Q}$-Gorenstein degenerations of projective space $\mathbb{P}^{n}$ and construct infinitely many new degenerations of projective space in any dimension. We also study in detail the deformations of arbitrary weighted projective threefolds. The rest of the paper provides several applications of the existence of degenerations of $\mathbb{P}^{n}$ and our methods apply to find many degenerations of $\mathbb{P}^{n}$ beyond just weighted projective spaces.