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Varieties of general type with the same Betti numbers as ℙ<sup>1</sup>× ℙ<sup>1</sup>×<i>⋯</i>× ℙ<sup>1</sup>

Varieties of general type with the same Betti numbers as ℙ<sup>1</sup>× ℙ<sup>1</sup>×<i>⋯</i>× ℙ<sup>1</sup>

We study quotients nH n of the n-fold product of the upper half-plane H by irreducible and torsion-free lattices < PSL 2 .R/ n with the same Betti numbers as the n-fold product .P 1 / n of projective lines.Such varieties are called fake products of projective lines or fake …