  Four-dimensional supersymmetric N = 1 vacua of type IIB supergravity are
elegantly described by generalized complex geometry. However, this approach
typically obscures the SL(2, R) covariance of the underlying theory. We show
how to rewrite the pure spinor equations of Grana, Minasian, Petrini and
Tomasiello (hep-th/0505212) in a manifestly SL(2,R) covariant fashion.
Solutions to these equations fall into two classes: "charged" solutions, such
as those containing D5-branes, and "chargeless" solutions, such as F-theory
solutions in the Sen limit and AdS4 solutions. We derive covariant
supersymmetry conditions for the chargeless case, allowing general SU(3)xSU(3)
structure. The formalism presented here greatly simplifies the study of the
ten-dimensional geometry of general supersymmetric compactifications of
F-theory.
