- in
algebraic geometry and
differential geometry,
Dolbeault cohomology (named
after Pierre Dolbeault) is an
analog of de Rham
cohomology for
complex manifolds...
-
Pierre Dolbeault (October 10, 1924 – June 12, 2015) was a
French mathematician.
Dolbeault studied with
Henri Cartan and
graduated in 1944 from the École...
-
projections defined in the
previous subsection, it is
possible to
define the
Dolbeault operators: ∂ = π p + 1 , q ∘ d : Ω p , q → Ω p + 1 , q , ∂ ¯ = π p , q...
-
obtains a
converse to the
construction of the
Dolbeault operator of a
holomorphic bundle: Theorem:
Given a
Dolbeault operator ∂ ¯ E {\displaystyle {\bar {\partial...
- set, the
boundary operator in a
chain complex, and the
conjugate of the
Dolbeault operator on
smooth differential forms over a
complex manifold. It should...
- ^{n},{\mathcal {O}}_{\mathbb {C} ^{n}}^{\star })} and we can
apply the
Dolbeault isomorphism to
calculate H 1 ( C n , O C n ) ≃ H 1 ( C n , Ω C n 0 ) ≃...
-
complex algebraic varieties, by an
application of
Dolbeault's theorem relating sheaf cohomology to
Dolbeault cohomology. Let X be a
smooth variety of dimension...
- form. Here ∂ , ∂ ¯ {\displaystyle \partial ,{\bar {\partial }}} are the
Dolbeault operators. The
function ρ {\displaystyle \rho } is
called a Kähler potential...
-
strong as a Kähler
metric on a
complex manifold, and the Hodge–Lefschetz–
Dolbeault theorems on
sheaf cohomology break down in
every possible way. In the...
- This is a
common generalization of the
Dirac operator (k = 1) and the
Dolbeault operator (n = 2, k arbitrary). It is an
invariant differential operator...
