On partially ample adjoint divisors

Abstract

We study the MMP (minimalmodelprogram )invarian tproperties of partially ample adjoint divisors. Using these invariant properties, we prove that th ethree notions of(numerically,cohomologically, asymptotically)partial ampleness coincide for big divisors on Q-factorial Fano type varieties and more generally Mori dream spaces.This gives a partial answer to a question raised by Totaro.