The log abundance conjecture asserts that a nef adjoint divisor 
of a projective log canonical
pair 
with rational boundary over an algebraically
closed field of characteristic
zero is a semiample divisor. Here 
is effective and 
is rational Cartier. The conclusion requires global generation
of an actual positive Cartier multiple, rather than only numerical positivity.
Log Abundance Conjecture
See also
Canonical Divisor, Canonical Nonvanishing Conjecture, Divisorial Log Terminal Pair, Iitaka Conjecture, Kaehler Manifold, Kawamata Log Terminal Pair, Log Canonical Pair, Minimal Model Program, Nef Divisor, Numerical Dimension, Semiample DivisorExplore with Wolfram|Alpha
References
Birkar, C. "Lectures on Birational Geometry." 9 Oct 2012. https://arxiv.org/abs/1210.2670.Cite this as:
Weisstein, Eric W. "Log Abundance Conjecture." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/LogAbundanceConjecture.html