Journal of the Mathematical Society of Japan

Quintic surfaces with maximum and other Picard numbers

Matthias SCHÜTT

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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

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

First available in Project Euclid: 27 October 2011

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Zentralblatt MATH identifier

Primary: 14J29: Surfaces of general type
Secondary: 11G40: $L$-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture [See also 14G10] 14G10: Zeta-functions and related questions [See also 11G40] (Birch- Swinnerton-Dyer conjecture) 14J50: Automorphisms of surfaces and higher-dimensional varieties

Picard number Delsarte surface automorphism zeta function


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.

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