Dwork family
From HandWiki
Short description: Family of hypersurfaces in algebraic geometry
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 given by the equations
- [math]\displaystyle{ x_1^n + x_2^n +\cdots +x_n^n = -n\lambda x_1x_2\cdots x_n \, , }[/math]
for all [math]\displaystyle{ n\ge 1 }[/math].
References
- Katz, Nicholas M. (2009), "Another look at the Dwork family", Algebra, arithmetic, and geometry: in honor of Yu. I. Manin. Vol. II, Progress in Mathematics, 270, Boston, MA: Birkhäuser Boston, pp. 89–126, http://www.math.princeton.edu/~nmk/dworkfam64.pdf
- ↑ Totaro, Burt (2007). "Euler and algebraic geometry". Bulletin of the American Mathematical Society 44 (4): 541–559. doi:10.1090/S0273-0979-07-01178-0. https://www.ams.org/journals/bull/2007-44-04/S0273-0979-07-01178-0/S0273-0979-07-01178-0.pdf. "p. 545".
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