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]

DefinitionEdit

The Dwork family is given by the equations

 

for all  .

ReferencesEdit

  • Katz, Nicholas M. (2009), "Another look at the Dwork family", Algebra, arithmetic, and geometry: in honor of Yu. I. Manin. Vol. II (PDF), Progress in Mathematics, 270, Boston, MA: Birkhäuser Boston, pp. 89–126, MR 2641188