  We consider global issues in minimal supergravity models where a single field
inflaton potential emerges. In a particular case we reproduce the Starobinsky
model and its description dual to a certain formulation of R+R^2 supergravity.
For definiteness we confine our analysis to spaces at constant curvature,
either vanishing or negative. Five distinct models arise, two flat models with
respectively a quadratic and a quartic potential and three based on the
SU(1,1)/U(1) space where its distinct isometries, elliptic, hyperbolic and
parabolic are gauged. Fayet-Iliopoulos terms are introduced in a geometric way
and they turn out to be a crucial ingredient in order to describe the de Sitter
inflationary phase of the Starobinsky model.
