Quintic surfaces with maximum and other Picard numbers

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.

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