# On Nonvanishing for uniruled log canonical pairs

## TL;DR

This paper proves the Nonvanishing conjecture for uniruled projective log canonical pairs assuming it for lower-dimensional smooth varieties, and links minimal model existence between uniruled and non-uniruled pairs.

## Contribution

It establishes the Nonvanishing conjecture for uniruled pairs based on lower-dimensional cases and connects minimal model existence across different pair types.

## Key findings

- Proves Nonvanishing for uniruled pairs assuming lower-dimensional cases.
- Shows minimal model existence for non-uniruled pairs implies it for all log canonical pairs.
- Links properties of uniruled and non-uniruled pairs in the minimal model program.

## Abstract

We prove the Nonvanishing conjecture for uniruled projective log canonical pairs of dimension $n$, assuming the Nonvanishing conjecture for smooth projective varieties in dimension $n-1$. We also show that the existence of good minimal models for non-uniruled projective klt pairs in dimension $n$ implies the existence of good minimal models for projective log canonical pairs in dimension $n$.