Bott-Chern cohomology is the cohomology of complex differential forms that are closed under both 
and 
, modulo forms in the image of 
. For a complex
manifold 
,
it is
 |
Here 
denotes smooth forms of type 
. In bidegree 
, its real version represents real closed forms modulo
of real smooth functions.
On a normal compact Kähler space, the corresponding real space can be defined with locally smooth potentials in local analytic embeddings. The analytic nef cone
is the closure of the Kähler cone in this space. Analytic pseudo-effectivity
instead requires a closed positive 
-current in the class, as used in compact Kähler minimal
model programs.
