Deformations of weak $\mathbb{Q}$-Fano 3-folds

Abstract

We prove that a weak $\mathbb{Q}$-Fano $3$-fold with terminal singularities has unobstructed deformations. By using this result and computing some invariants of a terminal singularity, we provide two results on global deformation of a weak $\mathbb{Q}$-Fano $3$-fold. We also treat a stacky proof of the unobstructedness of deformations of a $\mathbb{Q}$-Fano $3$-fold.

21 pages. Added several propositions about infinitesimal deformations. Deleted a section about a bound of singularities on a Q-Fano 3-fold. Instead, added a new section on Q-smoothability of a weak Q-Fano 3-fold

References in corpus (4)

• Differential Forms on Log Canonical Spaces
• Grothendieck Duality for Deligne-Mumford Stacks
• Deforming elephants of Q-Fano threefolds
• On deformations of Q-Fano threefolds II