# On minimal 4-folds of general type with $p_g \geq 2$

## TL;DR

This paper proves that for certain 4-dimensional algebraic varieties of general type with geometric genus at least 2, the 33-canonical map is birational and establishes a new lower bound for the canonical volume, improving previous results.

## Contribution

It establishes the birationality of the 33-canonical map and improves the lower bound for the canonical volume of minimal 4-folds of general type with p_g ≥ 2.

## Key findings

- 33-canonical map is birational onto its image
- Canonical volume has a lower bound of 1/520
- Improves previous bounds established by Chen and Chen

## Abstract

We show that, for nonsingular projective 4-folds V of general type with geometric genus $p_g\geq 2$, the 33-canonical map is birational onto the image and the canonical volume has the lower bound $1/520$, which improves a previous theorem by Chen and Chen.