Sentence examples for be a complex manifold from inspiring English sources

Let (X) be a complex manifold.

Let (X) be a complex manifold and (L rightarrow X) a holomorphic line bundle.

Let (X) be a complex manifold and (Z subset X) a hypersurface.

(Siu [49]) Let (X) be a complex manifold and (L rightarrow X) a holomorphic line bundle with singular Hermitian metric (e^{-varphi }) having non-negative curvature current.

To explain these, let (X)  be  a complex manifold, (iota : Z hookrightarrow X) a complex submanifold (or subvariety), and (L rightarrow X) a holomorphic line bundle.

Let X be a complex manifold which is homogeneous under the real analytic Lie group G where G is solvable with codimension one nilradical.

When equipped with, the manifold is a complex manifold.

Let p∈K and write for the stable manifold of f through p. is a complex manifold, say of complex dimension m.

A similar description holds in general (see [96], definition 4.4 and proposition 4.5, pp. 25 26 ), at least when Z is a complex manifold.

In this survey, we focus on classifying pairs ((X,G)) in the complex setting, i.e., when (X) is a complex manifold and (G) lies in the group (mathrm{Bihol}(X)) of biholomorphic automorphisms of (X).

Assuming, furthermore, that (X) is a complex manifold, we say that (G) acts on (X) by biholomorphisms  if (widehat{Phi }(G)) lies in the group (mathrm{Bihol}(X)) of all biholomorphic automorphisms of (X) (sometimes we refer to this group simply as the automorphism group).