On the non-vanishing conjecture and existence of log minimal models

TL;DR

This paper reduces the non-vanishing and log minimal model conjectures for projective log canonical pairs to the case of smooth projective varieties with zero boundary divisor, simplifying the approach to these conjectures.

Contribution

It establishes a reduction of key conjectures in algebraic geometry to a simpler case involving smooth projective varieties without boundary divisors.

Findings

Reduction of non-vanishing conjecture to smooth projective varieties

Reduction of log minimal model conjecture to smooth projective varieties

Simplification of approaches to log minimal models

Abstract

We prove that the non-vanishing conjecture and the log minimal model conjecture for projective log canonical pairs can be reduced to the non-vanishing conjecture for smooth projective varieties such that the boundary divisor is zero.