  It has been suggested that Type II supernovae with rapidly fading light
curves (a.k.a. Type IIL supernovae) are explosions of progenitors with low-mass
hydrogen-rich envelopes which are of the order of 1 Msun. We investigate
light-curve properties of supernovae from such progenitors. We confirm that
such progenitors lead to rapidly fading Type II supernovae. We find that the
luminosity of supernovae from such progenitors with the canonical explosion
energy of 1e51 erg and 56Ni mass of 0.05 Msun can increase temporarily shortly
before all the hydrogen in the envelope recombines. As a result, a bump appears
in their light curves. The bump appears because the heating from the nuclear
decay of 56Ni can keep the bottom of hydrogen-rich layers in the ejecta
ionized, and thus the photosphere can stay there for a while. We find that the
light-curve bump becomes less significant when we make explosion energy larger
(>~ 2e51 erg), 56Ni mass smaller (<~ 0.01 Msun), 56Ni mixed in the ejecta, or
the progenitor radius larger. Helium mixing in hydrogen-rich layers makes the
light-curve decline rates large but does not help reducing the light-curve
bump. Because the light-curve bump we found in our light-curve models has not
been observed in rapidly fading Type II supernovae, they may be characterized
by not only low-mass hydrogen-rich envelopes but also higher explosion energy,
larger degrees of 56Ni mixing, and/or larger progenitor radii than slowly
fading Type II supernovae, so that the light-curve bump does not become
significant.
