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In mathematics, a Barlow surface is one of the complex surfaces introduced by Rebecca Barlow (1984, 1985). They are simply connected surfaces of general type with pg = 0. They are homeomorphic but not diffeomorphic to a projective plane blown up in 8 points.

Hodge diamond:

1
0 0
0 9 0
0 0
1


See also

Hodge theory

References

Barlow, Rebecca (1984), "Some new surfaces with pg = 0", Duke Mathematical Journal 51 (4): 889–904, doi:10.1215/S0012-7094-84-05139-1, ISSN 0012-7094, MR 771386
Barlow, Rebecca (1985), "A simply connected surface of general type with pg = 0", Inventiones Mathematicae 79 (2): 293–301, doi:10.1007/BF01388974, ISSN 0020-9910, MR 778128
Barth, Wolf P.; Hulek, Klaus; Peters, Chris A.M.; Van de Ven, Antonius (2004), Compact Complex Surfaces, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. 4, Springer-Verlag, Berlin, ISBN 978-3-540-00832-3, MR 2030225
Kotschick, Dieter (1989), "On manifolds homeomorphic to CP2#8 CP2", Inventiones Mathematicae 95 (3): 591–600, doi:10.1007/BF01393892, ISSN 0020-9910, MR 979367

Mathematics Encyclopedia

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