Nakamaye's theorem on log canonical pairs

TL;DR

This paper extends Nakamaye's and Ein-Lazarsfeld-Mustata-Nakamaye-Popa's descriptions of base loci and augmented base loci to broader classes of pairs with log-canonical and klt singularities, using intersection theory and valuations.

Contribution

It generalizes existing descriptions of base loci to pairs with log-canonical and klt singularities, broadening the applicability of these geometric tools.

Findings

Extended Nakamaye's theorem to log-canonical pairs

Generalized valuation-based descriptions for klt pairs

Provided intersection-theoretic characterization of base loci

Abstract

We generalize Nakamaye's description, via intersection theory, of the augmented base locus of a big and nef divisor on a normal pair with log-canonical singularities or, more generally, on a normal variety with non-lc locus of dimension at most 1. We also generalize Ein-Lazarsfeld-Mustata-Nakamaye-Popa's description, in terms of valuations, of the subvarieties of the restricted base locus of a big divisor on a normal pair with klt singularities.