A JOURNEY FROM THE OCTONIONIC ℙ2 TO A FAKE ℙ2

Lev Borisov; Anders Buch; Enrico Fatighenti

doi:10.1090/proc/15840

A JOURNEY FROM THE OCTONIONIC ℙ² TO A FAKE ℙ²

Lev Borisov, Anders Buch, Enrico Fatighenti

Research output: Contribution to journal › Article › peer-review

Abstract

We discover a family of surfaces of general type with K² = 3 and p_g = 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.

Original language	English (US)
Pages (from-to)	1467-1475
Number of pages	9
Journal	Proceedings of the American Mathematical Society
Volume	150
Issue number	4
DOIs	https://doi.org/10.1090/proc/15840
State	Published - 2022
Externally published	Yes

All Science Journal Classification (ASJC) codes

Mathematics(all)
Applied Mathematics

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title = "A JOURNEY FROM THE OCTONIONIC ℙ2 TO A FAKE ℙ2",

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.",

author = "Lev Borisov and Anders Buch and Enrico Fatighenti",

note = "Funding Information: Received by the editors September 1, 2020, and, in revised form, July 27, 2021. 2020 Mathematics Subject Classification. Primary 14J29, 14Q10. The second author was partially supported by the NSF grant DMS-1503662. Publisher Copyright: {\textcopyright} 2022 American Mathematical Society",

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doi = "10.1090/proc/15840",

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N1 - Funding Information: Received by the editors September 1, 2020, and, in revised form, July 27, 2021. 2020 Mathematics Subject Classification. Primary 14J29, 14Q10. The second author was partially supported by the NSF grant DMS-1503662. Publisher Copyright: © 2022 American Mathematical Society

PY - 2022

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N2 - 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.

AB - 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.

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ER -

A JOURNEY FROM THE OCTONIONIC ℙ² TO A FAKE ℙ²

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