The canonical nonvanishing conjecture asserts that a smooth projective variety with pseudo-effective canonical divisor
has a nonzero pluricanonical section in some positive degree. It asks for 
from a numerical positivity condition, and by
itself does not require a globally generated multiple.
Canonical Nonvanishing Conjecture
See also
Canonical Divisor, Iitaka Dimension, Kodaira Dimension, Log Abundance Conjecture, Pseudo-Effective Divisor, Singular Hermitian MetricExplore 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. "Canonical Nonvanishing Conjecture." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/CanonicalNonvanishingConjecture.html