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Picard Numbers of Quintic Surfaces

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An algebraic surface is defined as the set of points that satisfy a polynomial equation . The Picard number for an algebraic surface is a measure of the complexity of the curves on the surface. Algebraic surfaces with Picard numbers 1 to 45 are presented according to [1] and [2] containing parameters and .

Contributed by: Enrique Zeleny (September 2013)
Open content licensed under CC BY-NC-SA

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More formally, the Picard number is the finite rank of the nonsingular complete variety of a sheaf cohomology group [3].

References

[1] M. Schuett, "Quintic Surfaces with Maximum and Other Picard Numbers." arxiv.org/abs/0812.3519.

[2] M. Schuett, "Picard Numbers of Quintic Surfaces." arxiv.org/abs/1308.2525.

[3] Wikipedia. "Picard Group." (May 6, 2013) en.wikipedia.org/wiki/Picard_group.

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