A closed immersion is a morphism of schemes 
that identifies 
with a closed subscheme
of 
.
It induces a homeomorphism from 
onto a closed set of 
, and the map of structure
sheaves 
is a surjection.
Locally, a closed immersion has the form 
for an ideal 
. Its kernel
sheaf is the ideal sheaf defining the closed
subscheme.
