  The interaction of supernova ejecta with a surrounding circumstellar medium
(CSM) generates a strong shock which can convert the ejecta kinetic energy into
observable radiation. Given the diversity of potential CSM structures (arising
from diverse mass loss processes such as late-stage stellar outbursts, binary
interaction, and winds), the resulting transients can display a wide range of
light curve morphologies. We provide a framework for classifying the transients
arising from interaction with a spherical CSM shell. The light curves are
decomposed into five consecutive phases, starting from the onset of interaction
and extending through shock breakout and subsequent shock cooling. The relative
prominence of each phase in the light curve is determined by two dimensionless
quantities representing the CSM-to-ejecta mass ratio $\eta$, and a breakout
parameter $\xi$. These two parameters define four light curve morphology
classes, where each class is characterized by the location of shock breakout
and the degree of deceleration as the shock sweeps up the CSM. We compile
analytic scaling relations connecting the luminosity and duration of each light
curve phase to the physical parameters. We then run a grid of radiation
hydrodynamics simulations for a wide range of ejecta and CSM parameters to
numerically explore the landscape of interaction light curves, and to calibrate
and confirm the analytic scalings. We connect our theoretical framework to
several case studies of observed transients, highlighting the relevance in
explaining slow-rising and superluminous supernovae, fast blue optical
transients, and double-peaked light curves.
