Explicit equations of a fake projective plane
| Autor: | Lev A. Borisov, JongHae Keum |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Surface (mathematics)
fake projective planes Pure mathematics Betti number General Mathematics 01 natural sciences Mathematics - Algebraic Geometry ball quotient equations elliptic surfaces 0103 physical sciences FOS: Mathematics Ball (mathematics) 0101 mathematics 14J29 Algebraic Geometry (math.AG) 32N15 Quotient Mathematics Complex conjugate 14J29 14F05 32Q40 32N15 Fake projective plane 14F05 010102 general mathematics Automorphism 32Q40 bicanonical embedding 010307 mathematical physics Projective plane |
| Zdroj: | Duke Math. J. 169, no. 6 (2020), 1135-1162 |
| ISSN: | 0012-7094 |
| DOI: | 10.1215/00127094-2019-0076 |
| Popis: | Fake projective planes are smooth complex surfaces of general type with Betti numbers equal to those of the usual projective plane. They come in complex conjugate pairs and have been classified as quotients of the two-dimensional ball by explicitly written arithmetic subgroups. In this paper we find equations of a projective model of a conjugate pair of fake projective planes by studying the geometry of the quotient of such surface by an order seven automorphism. Comment: This is a full version of "Research announcement: equations of a fake projective plane", arXiv:1710.04501. Key tables and some M2 and Magma code from the paper are included in separate files for convenience |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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