English

Picard numbers of quintic surfaces

Algebraic Geometry 2016-11-14 v2 Number Theory

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.

Keywords

Cite

@article{arxiv.1308.2525,
  title  = {Picard numbers of quintic surfaces},
  author = {Matthias Schuett},
  journal= {arXiv preprint arXiv:1308.2525},
  year   = {2016}
}

Comments

56 pages, 1 figure; v2: minor changes

R2 v1 2026-06-22T01:07:53.427Z