A Fano contraction is a projective surjective morphism 
of normal integral varieties with 
, rationally Cartier 
, and relatively ample anticanonical divisor 
. The condition on the structure sheaf
expresses connected fibers. The relative Picard number
need not be 1, and a birational contraction is allowed.
Fano Contraction
See also
Anticanonical Bundle, Bounded Klt Complement Conjecture, Cartier Divisor, Divisor Complement, Log DiscrepancyExplore with Wolfram|Alpha
References
Birkar, C. "Boundedness of Fano Type Fibrations." Ann. Sci. École Norm. Sup. 57, 787-840, 2024. https://doi.org/10.24033/asens.2582.Cite this as:
Weisstein, Eric W. "Fano Contraction." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/FanoContraction.html