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arXiv · 1308.2525

Picard numbers of quintic surfaces

Matthias Schuett
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Abstract

We solve the Picard number problem for complex quintic surfaces by proving that every number between 1 and 45 occurs as Picard number of a quintic surface over the rationals. Our main technique consists in arithmetic deformations of Delsarte surfaces, but we also use K3 surfaces and wild automorphisms.

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Matthias Schuett. 2014-09-21. Picard numbers of quintic surfaces. https://doi.org/10.1112/plms%2Fpdu056

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