We discover a family of surfaces of general type with K2 = 3 and pg = q = 0 as free C13 quotients of special linear cuts of the octonionic projective plane Oℙ2. A special member of the family has 3 singularities of type A2, 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.
Borisov L., Buch A., Fatighenti E. (2022). A JOURNEY FROM THE OCTONIONIC ℙ2 TO A FAKE ℙ2. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 150(4), 1467-1475 [10.1090/proc/15840].
A JOURNEY FROM THE OCTONIONIC ℙ2 TO A FAKE ℙ2
Fatighenti E.
2022
Abstract
We discover a family of surfaces of general type with K2 = 3 and pg = q = 0 as free C13 quotients of special linear cuts of the octonionic projective plane Oℙ2. A special member of the family has 3 singularities of type A2, 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.File in questo prodotto:
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FPPC13paper-revised-July2021.pdf
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