Cartwright, Donald I. and Steger, Tim Joshua (2010) Enumeration of the 50 fake projective planes = Énumération des 50 faux plans projectifs. Comptes rendus. Mathematique, Vol. 348 (1-2), p. 11-13. ISSN 1631-073X. Article.
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Building upon the classification of Prasad and Yeung [Invent. Math. 168 (2007) 321–370], we have shown that there exist exactly 50 fake projective planes (up to homeomorphism; 100 up to biholomorphism), and exhibited each of them explicitly as a quotient of the unit ball in C2. Some of these fake planes admit singular quotients by 3 element groups and three of these quotients are simply connected. Also exhibited are algebraic surfaces with c21=3c2=9n for any positive integer n.
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