  Argyres and Martone have produced a beautiful and deep classification of the
scale invariant Special Geometries in rank 2. They get a puzzle: the
scale-invariant geometries with Coulomb dimensions $\{2,2\}$ appear to depend
on four free complex parameters, while on physical grounds we expect only two
marginal deformations. We show that the isoclasses of $\{2,2\}$ Special
Geometries are indeed parametrized by a complex space of dimension 2, in facts
by a non-singular del Pezzo surface of degree 5, a result which exactly matches
the physical expectation by Gaiotto. This solves the puzzle.

High Energy Physics - Theory