Non-vanishing theorem for lc pairs admitting a Calabi--Yau pair

TL;DR

This paper proves the non-vanishing conjecture for log canonical pairs where the underlying variety is of Calabi--Yau type, advancing understanding in algebraic geometry and minimal model programs.

Contribution

It establishes the non-vanishing conjecture specifically for lc pairs with Calabi--Yau type varieties, a case previously unresolved.

Findings

Confirmed the non-vanishing conjecture for lc pairs of Calabi--Yau type

Extended the class of varieties where the conjecture holds

Provided new techniques applicable to Calabi--Yau pairs

Abstract

We prove the non-vanishing conjecture for lc pairs $(X,\Delta)$ when $X$ is of Calabi--Yau type.