  We present fits of generalized semi-analytic supernova (SN) light curve (LC)
models for a variety of power inputs including Ni-56 and Co-56 radioactive
decay, magnetar spin-down, and forward and reverse shock heating due to
supernova ejecta-circumstellar matter (CSM) interaction. We apply our models to
the observed LCs of the H-rich Super Luminous Supernovae (SLSN-II) SN 2006gy,
SN 2006tf, SN 2008am, SN 2008es, CSS100217, the H-poor SLSN-I SN 2005ap,
SCP06F6, SN 2007bi, SN 2010gx and SN 2010kd as well as to the interacting SN
2008iy and PTF09uj. Our goal is to determine the dominant mechanism that powers
the LCs of these extraordinary events and the physical conditions involved in
each case. We also present a comparison of our semi-analytical results with
recent results from numerical radiation hydrodynamics calculations in the
particular case of SN 2006gy in order to explore the strengths and weaknesses
of our models. We find that CS shock heating produced by ejecta-CSM interaction
provides a better fit to the LCs of most of the events we examine. We discuss
the possibility that collision of supernova ejecta with hydrogen-deficient CSM
accounts for some of the hydrogen-deficient SLSNe (SLSN-I) and may be a
plausible explanation for the explosion mechanism of SN 2007bi, the
pair-instability supernova (PISN) candidate. We characterize and discuss issues
of parameter degeneracy.
