English

Quintic surfaces with maximum and other Picard numbers

Algebraic Geometry 2011-09-20 v7 Number Theory

Abstract

This paper investigates the Picard numbers of quintic surfaces. We give the first example of a complex quintic surface in IP^3 with maximum Picard number 45. We also investigate its arithmetic and determine the zeta function. Similar techniques are applied to produce quintic surfaces with several other Picard numbers that have not been achieved before.

Keywords

Cite

@article{arxiv.0812.3519,
  title  = {Quintic surfaces with maximum and other Picard numbers},
  author = {Matthias Schuett},
  journal= {arXiv preprint arXiv:0812.3519},
  year   = {2011}
}

Comments

13 pages; typo in table 1 corrected thanks to Xavier Roulleau

R2 v1 2026-06-21T11:53:34.401Z