Dwork family

Template:Short description 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

$x_1^n+x_2^n+\cdots +x_n^n=-n\lambda x_1{x}_2\cdots x_n,$

for all $n\ge 1$.

History

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

References

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