## Journal of the Mathematical Society of Japan

### Quintic surfaces with maximum and other Picard numbers

Matthias SCHÜTT

#### Abstract

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.

#### Article information

Source
J. Math. Soc. Japan, Volume 63, Number 4 (2011), 1187-1201.

Dates
First available in Project Euclid: 27 October 2011

https://projecteuclid.org/euclid.jmsj/1319721139

Digital Object Identifier
doi:10.2969/jmsj/06341187

Mathematical Reviews number (MathSciNet)
MR2855811

Zentralblatt MATH identifier
1232.14022

#### Citation

SCHÜTT, Matthias. Quintic surfaces with maximum and other Picard numbers. J. Math. Soc. Japan 63 (2011), no. 4, 1187--1201. doi:10.2969/jmsj/06341187. https://projecteuclid.org/euclid.jmsj/1319721139

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