2014
DOI: 10.2422/2036-2145.201109_004
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The Barth quintic surface has Picard number 41

Abstract: This paper investigates a specific smooth quintic surface suggested by Barth for it contains the current record of 75 lines over the complex numbers. Our main incentive is to prove that the complex quintic has Picard number 41, and to compute the Néron-Severi group up to a 2-power index. We also compute Picard numbers for reductions to positive characteristic and verify the Tate conjecture.

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Cited by 2 publications
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“…Zhang, whereas his published and unpublished examples appear in various contexts in algebraic geometry (e.g. Barth's quintics surface with 75 lines turns out to be the smooth quintic with the highest Picard number known so far -see [64]).…”
Section: Symmetriesmentioning
confidence: 99%

Wolf Barth (1942--2016)

Bauer,
Hulek,
Rams
et al. 2017
Preprint
Self Cite
“…Zhang, whereas his published and unpublished examples appear in various contexts in algebraic geometry (e.g. Barth's quintics surface with 75 lines turns out to be the smooth quintic with the highest Picard number known so far -see [64]).…”
Section: Symmetriesmentioning
confidence: 99%

Wolf Barth (1942--2016)

Bauer,
Hulek,
Rams
et al. 2017
Preprint
Self Cite