fake projective space

{{Short description|Complex algebraic variety}}

In mathematics, a fake projective space is a complex algebraic variety that has the same Betti numbers as some projective space, but is not isomorphic to it.

There are exactly 50 fake projective planes. {{harvtxt|Prasad|Yeung|2006}} found four examples of fake projective 4-folds, and showed that no arithmetic examples exist in dimensions other than 2 and 4.