Some results on fake quadrics

Abstract

In this paper, we obtain several results on fake quadrics. First, we describe the cones \(\operatorname{Nef}(S)\) and \(\overline{\operatorname{Eff}(S)}\), and then provide a criterion for determining whether a divisor on a fake quadric is ample or effective, respectively. Second, we show that no fake quadric can be embedded into ${\mathbb{P}}^4$. Finally, we establish the bounded cohomology property for fake quadrics.

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