On Fujita's conjecture for pseudo-effective thresholds

TL;DR

This paper proves conjectures related to Fujita's spectrum and log spectrum for certain pairs, and extends the concept of pseudo-effective thresholds to multiple divisors, establishing key finiteness and DCC properties.

Contribution

It proves Fujita's spectrum and log spectrum conjectures for specific pairs and generalizes pseudo-effective thresholds to multiple divisors with important finiteness results.

Findings

Proved Fujita's spectrum conjecture for epsilon-log canonical pairs.

Established finiteness and DCC properties for generalized pseudo-effective thresholds.

Extended the concept of pseudo-effective thresholds to multiple divisors.

Abstract

We show Fujita's spectrum conjecture for $\epsilon$-log canonical pairs and Fujita's log spectrum conjecture for log canonical pairs. Then, we generalize the pseudo-effective threshold of a single divisor to multiple divisors and establish the analogous finiteness and the DCC properties.