We study the MMP (minimal model program) invariant properties of partially ample adjoint divisors. Using these invariant properties, we prove that the three 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.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory