On the canonical degrees of Gorenstein threefolds of general type

TL;DR

This paper improves the universal bound on the canonical degree of Gorenstein minimal projective threefolds of general type from 576 to 360 and classifies possible degrees for abelian covers over projective 3-space.

Contribution

The authors significantly tighten the universal bound on the canonical degree and classify all possible degrees for a specific class of threefolds, providing explicit examples.

Findings

Universal bound on canonical degree improved to 360.

Complete classification of canonical degrees for abelian covers over P^3.

Constructed explicit examples for all possible degrees.

Abstract

Let $X$ be a Gorenstein minimal projective $3$-fold with at worst locally factorial terminal singularities. Suppose that the canonical map is generically finite onto its image. C. Hacon showed that the canonical degree is universally bounded by $576$. We improved Hacon's universal bound to $360$. Moreover, we gave all the possible canonical degrees of $X$ if $X$ is an abelian cover over $\mathbb{P}^3$ and constructed all the examples with these canonical degrees.