# Varieties of general type with small volumes

## TL;DR

This paper constructs examples of higher-dimensional algebraic varieties of general type with small volumes, extending known inequalities and providing new insights into their geometric properties.

## Contribution

It generalizes Kobayashi's example to higher dimensions, demonstrating the existence of n-folds of general type with small volumes.

## Key findings

- Examples of n-folds of general type with small volumes
- Extension of Noether inequality to higher dimensions
- New geometric properties of algebraic varieties

## Abstract

Generalize Kobayashi's example for the Noether inequality in dimension three, we provide examples of n-folds of general type with small volumes.