Abstract
We give an effective bound of the Gorenstein index of weak $\mathbf{Q}$-Fano 3-folds, and prove the boundedness of the terminal $\mathbf{Q}$-Fano 3-folds. Combined with [Bor99], this result implies furthermore the boundedness of the canonical $\mathbf{Q}$-Fano 3-folds.
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