  Large synoptic (repeated scan) imaging sky surveys are poised to observe
enormous numbers of core-collapse supernovae. We quantify the discovery
potential of upcoming projects, including DES, Pan-STARRS, and LSST. These
surveys will map out the cosmic core-collapse supernova redshift distribution
via direct counting, with very small statistical uncertainties out to a
redshift depth which is a strong function of the survey limiting magnitude.
This supernova redshift history encodes rich information about cosmology, star
formation, and supernova astrophysics and phenomenology; the large statistics
of the supernova sample will be crucial to disentangle possible degeneracies
among these issues. For example, the cosmic supernova rate can be measured to
high precision out to z ~ 0.5 for all core-collapse types, and out to redshift
z ~ 1 for Type IIn events. Because of the tight link between supernovae and
star formation, synoptic sky surveys will provide precision measurements of the
normalization and z < 1 history of cosmic star-formation rate in a manner
independent of and complementary to current methods. Furthermore, Type II
supernovae can serve as distance indicators and would independently cross-check
Type Ia distances measured in the same surveys. Arguably the largest and
least-controlled uncertainty in these efforts comes from dust obscuration of
supernovae in their host galaxies; we outline a strategy to determine
empirically the obscuration properties by leveraging the large supernova
samples over a broad range of redshift. [abstract abridged]
