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Dwork family

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In algebraic geometry, a Dwork family is a one-parameter family of hypersurfaces depending on an integer n, studied by Bernard Dwork. Originally considered by Dwork in the context of local zeta-functions, such families have been shown to have relationships with mirror symmetry and extensions of the modularity theorem.

Definition

The Dwork family is

x 1 n + x 2 n + + x n n = n λ x 1 x 2 x n

References

Dwork family Wikipedia