Journal of the Mathematical Society of Japan

Quintic surfaces with maximum and other Picard numbers

Matthias SCHÜTT

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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

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1319721139

Digital Object Identifier
doi:10.2969/jmsj/06341187

Mathematical Reviews number (MathSciNet)
MR2855811

Zentralblatt MATH identifier
1232.14022

Subjects
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

Keywords
Picard number Delsarte surface automorphism zeta function

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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