Dwork family

Dwork family

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.[1]

Definition

The Dwork family is

 x_1^n + x_2^n +\cdots +x_n^n = -n\lambda x_1x_2\cdots x_n \,

References


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