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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
##### Keywords:
canonical volume; 3-folds of general type
Full Text:
##### References:
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