Seiberg-Witten theory provides a geometric understanding of N=2 gauge theories while Conformal invariance further constrains the Coulomb branch to be scale-invariant. We will show that this picture is richer: Coulomb branch deformations are related in a precise way to the spectrum of relevant, irrelevant and marginal operators of the SCFT. In particular, a careful study of the former can constraint the latter, geometric constraints on the space of possible N=2 SCFTs can be extracted and a classification scheme can be outlined. In particular, we carry out this program for the rank 1 case.

Some of the constraints on the space of SCFTs which can be obtained in a straightforward way with our approach are instead harder to extract using bootstrap techniques. These two approaches should be thus seen as complementary to one another.