Journal of the Mathematical Society of Japan
- J. Math. Soc. Japan
- Volume 63, Number 4 (2011), 1187-1201.
Quintic surfaces with maximum and other Picard numbers
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.
J. Math. Soc. Japan, Volume 63, Number 4 (2011), 1187-1201.
First available in Project Euclid: 27 October 2011
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
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
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