A journey from the octonionic ℙ² to a fake ℙ²

Borisov, Lev; Buch, Anders; Fatighenti, Enrico

doi:10.1090/proc/15840

A journey from the octonionic $\mathbb P^2$ to a fake $\mathbb P^2$
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by Lev Borisov, Anders Buch and Enrico Fatighenti PDF

Proc. Amer. Math. Soc. 150 (2022), 1467-1475 Request permission

Abstract:

We discover a family of surfaces of general type with $K^2=3$ and $p_g=q=0$ 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 earlier work of Borisov and Fatighenti to define this fake projective plane by explicit equations in its bicanonical embedding.

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