  Core-collapse SNe (CCSNe): Systematic searches of radio emission from CCSNe
are still lacking, and only targeted searches of radio emission from just some
of the optically discovered CCSNe in the local universe have been carried out.
Optical searches miss a significant fraction of CCSNe due to dust obscuration;
CCSN radio searches are thus more promising for yielding the complete,
unobscured star-formation rates in the local universe. The SKA yields the
possibility to piggyback for free in this area of research by carrying out
commensal, wide-field, blind transient survey observations. SKA1-SUR should be
able to discover several hundreds of CCSNe in just one year, compared to about
a dozen CCSNe that the VLASS would be able to detect in one year, at most. SKA,
with an expected sensitivity ten times that of SKA1, is expected to detect
CCSNe in the local Universe by the thousands. Therefore, commensal SKA
observations could easily result in an essentially complete census of all CCSNe
in the local universe, thus yielding an accurate determination of the
volumetric CCSN rate. Type Ia SNe: We advocate for the use of the SKA to search
for the putative prompt (~first few days after the explosion) radio emission of
any nearby type Ia SN, via target-of-opportunity observations. The huge
improvement in sensitivity of the SKA with respect to its predecessors will
allow to unambiguously discern which progenitor scenario (single-degenerate vs.
double-degenerate) applies to them.
