Comparison and uniruledness of asymptotic base loci

TL;DR

This paper proves that the asymptotic base loci of certain generalized pairs are uniruled and establishes their relation with non-nef and diminished base loci, advancing understanding in algebraic geometry.

Contribution

It demonstrates uniruledness of asymptotic base loci for NQC klt generalized pairs and shows the equivalence of non-nef and diminished base loci for adjoint divisors.

Findings

Asymptotic base loci of NQC klt generalized pairs are uniruled.

Non-nef locus and diminished base locus coincide for adjoint divisors.

Applications to uniruledness of base loci on generalized log Calabi-Yau varieties.

Abstract

We prove that the asymptotic base loci of an NQC klt generalized pair with big canonical class are uniruled. We also show that the non-nef locus and the diminished base locus of the adjoint divisor of an NQC log canonical generalized pair coincide. As applications, we study the uniruledness of the asymptotic base loci associated with pseudo-effective divisors on generalized log Calabi-Yau type varieties.