Dolbeault cohomology

In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, in particular in <a href="/facts/Algebraic_geometry/rh7RHVp3">algebraic geometry</a> and <a href="/facts/Differential_geometry/c04XmyLu">differential geometry</a>, Dolbeault cohomology (named after <a href="/facts/Pierre_Dolbeault/qL9h8QoH">Pierre Dolbeault</a>) is an analog of <a href="/facts/De_Rham_cohomology/4qGKeJq0">de Rham cohomology</a> for <a href="/facts/Complex_manifold/DlvPnpzm">complex manifolds</a>. Let M be a complex manifold. Then the Dolbeault cohomology groups 
 
 
 
 
 H
 
 p
 ,
 q
 
 
 (
 M
 ,
 
 C
 
 )
 
 
 {\displaystyle H^{p,q}(M,\mathbb {C} )}
 
 depend on a pair of integers p and q and are realized as a subquotient of the space of <a href="/facts/Complex_differential_form/307vM8pd">complex differential forms</a> of degree (p,q).

Dolbeault cohomology open-in-new

Dolbeault cohomology