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A sharp lower bound for the canonical volume of 3-folds of general type. (English) Zbl 1124.14038
The main result of the paper under review is the following:
If \(V\) is a smooth projective 3-fold of general type with \(p_g(V)\geq 2\) (resp. \(p_g(V)\geq 3\) and \(p_g(V)\geq 4\)), then the canonical volume of \(V\) is at least \(1/3\) (resp. at least \(1\) and \(2\)).
It is also shown that the above bounds are sharp and the geometry of \(3\)-folds with \(p_g(V)\geq 2\) and small canonical volume are studied in detail.

MSC:
14J30 \(3\)-folds
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