  We report on the discovery and analysis of short-period (0.1 days $< P <$ 5
days), photometrically varying binary stars around and below the main-sequence
turnoff of the globular clusters (GCs) NGC 3201, M10, & M12. These eclipsing
binaries (EBs) may be used to determine directly the distances to GCs and
constrain the Population II stellar main-sequence masses. During our search for
binaries, we discovered the signature of differential reddening across the
cluster fields which was especially strong for NGC 3201 and M10. We correct for
this differential reddening by calculating average $E_{V-I}$ values for stars
in small subregions of the field with respect to a fiducial region, which
significantly improves the appearance of the GC color-magnitude diagrams
(CMDs). The reddening zero point to be added to the differential value is
determined by isochrone fitting. The results of our differential dereddening
are presented in the form of high-resolution extinction maps. Our search for
EBs returned 14 variable stars (11 EBs) in the field of NGC 3201, 3 variables
(1 EB) in M10, and 2 EBs in M12. Of these variables, only one EB in NGC 3201 (a
blue straggler W Ursa Majoris contact system) is a definite GC-member, based on
spectroscopic observations. Another W UMa contact EB in M12 is most likely a
member of M12, based on its location in the color-magnitude diagram (CMD) and
its empirically calculated absolute magnitude. We present the phased
lightcurves for all variables, estimate their distances and GC membership, and
show their locations in the GC fields and CMDs, as well as the spectra of the
NGC 3201 EBs. Finally, we discuss the implications of our results and outline
future work.
