A Fano type variety is a normal projective variety admitting an effective rational boundary 
such that 
is Kawamata log terminal and 
is ample. The relative notion uses ampleness over a
base and enters Fano type contractions. A
smooth Fano manifold satisfies this definition with
zero boundary, while Fano type allows singular varieties and a nonzero witnessing
boundary.
Fano Type Variety
See also
Fano Manifold, Fano Type Contraction, Kawamata Log Terminal PairExplore 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 Type Variety." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/FanoTypeVariety.html