Benveniste, X. Sur les applications pluricanoniques des variétés de type très général en dimension 3. (On the pluricanonical mappings of varieties of very general type in dimension 3). (French) Zbl 0601.14035 Am. J. Math. 108, 433-449 (1986). As is well-known, there exist universal bounds on the multiple of the canonical divisor, effecting a birational embedding of a variety of general type, in the cases of curves and surfaces. For threefolds and higher varieties such universal bounds are not known, and they may very well not exist. One of the new difficulties encountered for threefolds is that the canonical divisor may not be numerically positive. The author introduces the concept of a very general threefold (... de type très général) if the canonical divisor is numerically positive (in the sense of the author’s paper ”Sur la décomposition en dimension 3”, to appear). The main result of the paper is to show that the nine canonical maps always embed birationally. The author also lists possible exceptions for the failure of this in the seven and eight canonical case. Reviewer: U.Persson Cited in 4 ReviewsCited in 14 Documents MSC: 14J30 \(3\)-folds 14C20 Divisors, linear systems, invertible sheaves Keywords:numerically positive canonical divisor; very general threefold; canonical maps × Cite Format Result Cite Review PDF Full Text: DOI