On bicanonical maps of threefolds of general type with large volumes

TL;DR

This paper investigates the properties of bicanonical maps of threefolds of general type with large canonical volume, establishing a lower bound on the dimension of their images and exploring related pluricanonical maps.

Contribution

It proves a lower bound on the dimension of the image of bicanonical maps for threefolds with large volume and studies pluricanonical maps of fibered threefolds.

Findings

Bicanonical map image dimension is at least 2 for volumes > 12^6.

Analyzes pluricanonical maps of fibered threefolds with specific surface types.

Provides new bounds and structural insights for threefolds of large volume.

Abstract

We prove that for any smooth projective $3$-fold of general type with canonical volume greater than $12^6$, the image of its bicanonical map has dimension at least $2$. We also study pluricanonical maps of $3$-folds of general type with large canonical volume and fibered by $(1,2)$-surfaces or $(2,3)$-surfaces.