The Barth quintic surface has Picard number 41

Details The Barth quintic surface has Picard number 41 The Barth quintic surface has Picard number 41

2011-07-12

arxiv.org/abs/1107.2210v1

Mathematics

Algebraic Geometry

12 pages

Scientific paper

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. We
also compute Picard numbers for reductions to positive characteristic and
verify the Tate conjecture.

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