Quintic surfaces with maximum and other Picard numbers

Details Quintic surfaces with maximum and other Picard numbers Quintic surfaces with maximum and other Picard numbers

2008-12-18

arxiv.org/abs/0812.3519v7

Mathematics

Algebraic Geometry

13 pages; typo in table 1 corrected thanks to Xavier Roulleau

Scientific paper

This paper investigates the Picard numbers of quintic surfaces. We give the
first example of a complex quintic surface in IP^3 with maximum Picard number
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.

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