On the canonical maps of nonsingular threefolds of general type

TL;DR

This paper extends Beauville's results on the canonical maps from surfaces to threefolds, analyzing the properties and degrees of the canonical map for nonsingular minimal complex projective threefolds of general type.

Contribution

It generalizes Beauville's findings on canonical maps from surfaces to threefolds, providing new insights into their geometric properties.

Findings

Canonical map degrees are characterized for threefolds.

The geometric genus of the image of the canonical map is either zero or equals that of the threefold.

Results extend known surface theory to three-dimensional varieties.

Abstract

Let $S$ be a nonsingular minimal complex projective surface of general type and the canonical map of $S$ is generically finite. Beauville showed that the geometric genus of the image of the canonical map is vanishing or equals the geometric genus of $S$ and discussed the canonical degrees for these two cases. We generalize his results to nonsingular minimal complex projective threefolds.