  Let A be an affine variety inside a complex N dimensional vector space which
has an isolated singularity at the origin. The intersection of A with a very
small sphere turns out to be a contact manifold called the link of A. Any
contact manifold contactomorphic to the link of A is said to be Milnor fillable
by A. If the first Chern class of our link is torsion then we can assign an
invariant of our singularity called the minimal discrepancy, which is an
important invariant in birational geometry. We define an invariant of the link
up to contactomorphism using Conley-Zehnder indices of Reeb orbits and then we
relate this invariant with the minimal discrepancy. As a result we show that
the standard contact 5 dimensional sphere has a unique Milnor filling up to
normalization proving a conjecture by Seidel.
