A journey from the octonionic ${\mathbb{P}}^2$ to a fake ${\mathbb{P}}^2$

Abstract

We discover a family of surfaces of general type with $K^2=3$ and $p=q=0$ as free $C_{13}$ quotients of special linear cuts of the octonionic projective plane $\mathbb{O}{\mathbb{P}}^2$. A special member of the family has $3$ singularities of type $A_2$, and is a quotient of a fake projective plane. We use the techniques of \cite{BF20} to define this fake projective plane by explicit equations in its bicanonical embedding.

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References in corpus (1)

• New explicit constructions of surfaces of general type