A terminal singularity is a singularity of a normal variety 
over a field of characteristic
zero with rational Cartier divisor 
for which every exceptional prime
divisor has positive discrepancy. Here 
is the canonical divisor.
On a smooth birational model 
, write
 |
The condition is 
for every exceptional divisor 
on every such model (Kollár and Mori 1998).
The associated log discrepancies are 
, so a variety with terminal singularities and zero boundary
is a log canonical pair. Smooth algebraic
varieties have terminal singularities in this discrepancy sense, which includes
nonsingular points.
