Pluricanonical systems for 3-folds and 4-folds of general type
Lorenzo Di Biagio
TL;DR
This paper establishes explicit lower bounds on the volume of threefolds and fourfolds of general type to ensure nonvanishing and birationality of pluricanonical systems, providing criteria for the birationality of the fourth canonical map in large volume cases.
Contribution
It offers new explicit volume bounds and criteria for pluricanonical map properties in threefolds and fourfolds of general type, advancing understanding of their birational geometry.
Findings
Lower bounds on volume for nonvanishing of pluricanonical systems
Conditions for the birationality of the fourth canonical map in large volume threefolds
Explicit criteria for pluricanonical map properties in higher-dimensional varieties
Abstract
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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