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.

Definition

The Dwork family is given by the equations
for all.

History

The Dwork family was originally used by B. Dwork to develop the deformation theory of zeta functions of nonsingular hypersurfaces in projective space.