The anticanonical nonvanishing conjecture in the positive-multiple formulation asks whether a smooth projective complex variety with nef anticanonical bundle has a nonzero section of some positive power. It asks for linear effectivity of the specified bundle, which is stronger than representing its numerical class by an effective divisor.
Anticanonical Nonvanishing Conjecture
See also
Anticanonical Bundle, Equivariant Line Bundle, Kawamata Log Terminal Pair, Nef Line Bundle, Pseudo-Effective Divisor, Semipositive Line BundleExplore with Wolfram|Alpha
References
Lazić, V.; Matsumura, S.; Peternell, Th.; Tsakanikas, N.; and Xie, Z. "The Nonvanishing Problem for Varieties with Nef Anticanonical Bundle." Doc. Math. 28, 1393-1440, 2023. https://doi.org/10.4171/DM/936.Cite this as:
Weisstein, Eric W. "Anticanonical Nonvanishing Conjecture." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/AnticanonicalNonvanishingConjecture.html