Fake projective space
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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. (Prasad Yeung) 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, Bibcode: 2006math......2144P, http://www.mpim-bonn.mpg.de/preprints/send?bid=3351
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