  Metrics on Calabi-Yau manifolds are used to derive a formula that finds the
existence of integer solutions to polynomials. These metrics are derived from
an associated algebraic curve, together with its anti-holomorphic counterpart.
The integer points in the curve coincide with points on the manifold, and the
metric form around these points are used to find their existence. The explicit
form of the metrics can be found through a solution to the D-terms in a
non-linear sigma model.
