Non-vanishing theorem for generalized log canonical pairs with a polarization

TL;DR

This paper proves the non-vanishing conjecture for a class of generalized log canonical pairs with a polarization, advancing the understanding of their geometric properties.

Contribution

It establishes the non-vanishing theorem specifically for generalized lc pairs with polarization, a new result in the field.

Findings

Non-vanishing conjecture holds for generalized lc pairs with polarization.

Provides new tools for studying the geometry of polarized pairs.

Advances the minimal model program for these pairs.

Abstract

We prove that the non-vanishing conjecture holds for generalized lc pairs with a polarization.