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Exceptional collections and the bicanonical map of Keum’s fake projective planes

Gennaro Di Brino

Max Planck Institute for Mathematics, Germany

E-mail Address: gennaro.dibrino@gmail.com

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and

Luca F. Di Cerbo

International Centre for Theoretical Physics, Italy

E-mail Address: ldicerbo@ictp.it

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https://doi.org/10.1142/S0219199716500668Cited by:3 (Source: Crossref)

Abstract

We apply the recent results of Galkin et al. [Derived categories of Keum’s fake projective planes, Adv. Math.278 (2015) 238–253] to study some geometrical features of Keum’s fake projective planes. Among other things, we show that the bicanonical map of Keum’s fake projective planes is always an embedding. Moreover, we construct a nonstandard exceptional collection on the unique fake projective plane $X$ $X$ with $H_{1} (X; ℤ) = {(ℤ / 2 ℤ)}^{4}$ .

Keywords:

AMSC: 14J29, 14F05

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