  Hochster and Huneke showed that the property of F-regularity deforms for
Gorenstein rings, i.e., if (R,m) is a Gorenstein local ring such that R/tR is
F-regular for some nonzerodivisor t in m, then R is F-regular. This result was
later extended to the case of Q-Gorenstein rings by Smith (for rings of
characteristic zero) and Aberbach, Katzman, and MacCrimmon (for rings of
positive characteristic). We investigate the deformation of strong F-regularity
using an anti-canonical cover of R, i.e., a symbolic Rees algebra S = R + It +
I^(2)t^2 + ..., where I is an inverse for the canonical module in the divisor
class group of the ring R. We show that strong F-regularity deforms in the case
that the symbolic powers I^(i) satisfy the Serre condition S_3 for all i > 0,
and the ring S is Noetherian. We also construct examples which show that the
property of F-purity does not deform.
