This paper investigates the Picard numbers of quintic surfaces. We give the first example of a complex quintic surface in P3 with maximum Picard number ρ = 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.
"Quintic surfaces with maximum and other Picard numbers." J. Math. Soc. Japan 63 (4) 1187 - 1201, October, 2011. https://doi.org/10.2969/jmsj/06341187