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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. 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.

References

• Prasad, Gopal; Yeung (2006), Fake Projective spaces, preprint, MPIM-Bonn, arXiv:math/0602144, Bibcode:2006math......2144P

• Algebraic geometry