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

TL;DR

This paper proves that weak $Q$-Fano 3-folds with terminal singularities have unobstructed deformations, and explores their global deformation properties using invariants and stack-theoretic methods.

Contribution

It establishes the unobstructedness of deformations for weak $Q$-Fano 3-folds and provides new results on their global deformation behavior.

Findings

Unobstructed deformations of weak $Q$-Fano 3-folds with terminal singularities.

Computed invariants of terminal singularities relevant to deformation theory.

Stacky proof of deformation unobstructedness for $Q$-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.