  Using the OSIRIS instrument installed on the 10.4-m Gran Telescopio Canarias
(GTC) we acquired multi-color transit photometry of four small (Rp < 5 R_Earth)
short-period (P < 6 days) planet candidates recently identified by the Kepler
space mission. These observations are part of a program to constrain the false
positive rate for small, short-period Kepler planet candidates. Since planetary
transits should be largely achromatic when observed at different wavelengths
(excluding the small color changes due to stellar limb darkening), we use the
observed transit color to identify candidates as either false positives (e.g.,
a blend with a stellar eclipsing binary either in the background/foreground or
bound to the target star) or validated planets. Our results include the
identification of KOI 225.01 and KOI 1187.01 as false positives and the
tentative validation of KOI 420.01 and KOI 526.01 as planets. The probability
of identifying two false positives out of a sample of four targets is less than
1%, assuming an overall false positive rate for Kepler planet candidates of 10%
(as estimated by Morton & Johnson 2011). Therefore, these results suggest a
higher false positive rate for the small, short-period Kepler planet candidates
than has been theoretically predicted by other studies which consider the
Kepler planet candidate sample as a whole. Furthermore, our results are
consistent with a recent Doppler study of short-period giant Kepler planet
candidates (Santerne et al. 2012). We also investigate how the false positive
rate for our sample varies with different planetary and stellar properties. Our
results suggest that the false positive rate varies significantly with orbital
period and is largest at the shortest orbital periods (P < 3 days), where there
is a corresponding rise in the number of detached eclipsing binary stars...
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