Abstract
We study quotients of the –fold product of the upper half-plane by irreducible and torsion-free lattices with the same Betti numbers as the –fold product of projective lines. Such varieties are called fake products of projective lines or fake . These are higher-dimensional analogs of fake quadrics. In this paper we show that the number of fake is finite (independently of ), we give examples of fake and show that for there are no fake of the form with contained in the norm-one group of a maximal order of a quaternion algebra over a real number field.
Citation
Amir Džambić. "Varieties of general type with the same Betti numbers as $\mathbb{P}^1\times \mathbb{P}^1\times\cdots\times \mathbb{P}^1$." Geom. Topol. 19 (4) 2257 - 2276, 2015. https://doi.org/10.2140/gt.2015.19.2257
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