The anticanonical bundle of a smooth variety or complex manifold 
is the dual 
of its canonical bundle 
. Its divisor class is the negative
of the canonical class. A smooth projective variety
whose anticanonical bundle is ample is called a Fano variety.
Smooth semipositivity of the anticanonical bundle means that it admits a smooth Hermitian metric with nonnegative
Chern curvature.
See also
Anticanonical Linear System,
Anticanonical Nonvanishing Conjecture,
Canonical Bundle,
Divisor,
Fano Contraction,
Fano
Index,
Fano Manifold,
Fano
Pseudoindex,
Fano Type Variety,
Line
Bundle,
Semipositive Line Bundle,
Vector Bundle
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References
Hartshorne, R. Algebraic
Geometry. New York: Springer-Verlag, 1977.
Cite this as:
Weisstein, Eric W. "Anticanonical Bundle."
From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/AnticanonicalBundle.html
Subject classifications
