Pluricanonical systems for 3-folds and 4-folds of general type

Details Pluricanonical systems for 3-folds and 4-folds of general type Pluricanonical systems for 3-folds and 4-folds of general type

2010-01-19

arxiv.org/abs/1001.3340v2

Math. Proc. Camb. Phil. Soc. (2012), vol. 152, issue 01, pp. 9-34

Mathematics

Algebraic Geometry

25 pages. Minor corrections and improved exposition. To appear in Mathematical Proceedings of the Cambridge Philosophical Soci

Scientific paper

10.1017/S0305004111000648

We explicitly find lower bounds on the volume of threefolds and fourfolds of
general type in order to have nonvanishing of pluricanonical systems and
birationality of pluricanonical maps. In the case of threefolds of large
volume, we also give necessary and sufficient conditions for the fourth
canonical map to be birational.

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