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- W2056578192 abstract "Nonsingular projective 3-folds $V$ of general type can be naturally classified into 18 families according to the pluricanonical section index ${itdelta}(V):=text{min}{mmid P_{m}geqslant 2}$ since $1leqslant {itdelta}(V)leqslant 18$ due to our previous series (I, II). Based on our further classification to 3-folds with ${itdelta}(V)geqslant 13$ and an intensive geometrical investigation to those with ${itdelta}(V)leqslant 12$ , we prove that $text{Vol}(V)geqslant frac{1}{1680}$ and that the pluricanonical map ${rmPhi}_{m}$ is birational for all $mgeqslant 61$ , which greatly improves known results. An optimal birationality of ${rmPhi}_{m}$ for the case ${itdelta}(V)=2$ is obtained. As an effective application, we study projective 4-folds of general type with $p_{g}geqslant 2$ in the last section." @default.
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- W2056578192 date "2014-12-30" @default.
- W2056578192 modified "2023-10-12" @default.
- W2056578192 title "Explicit birational geometry of 3-folds and 4-folds of general type, III" @default.
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