complex submanifold
1Complex manifold — In differential geometry, a complex manifold is a manifold with an atlas of charts to the open unit disk[1] in Cn, such that the transition maps are holomorphic. The term complex manifold is variously used to mean a complex manifold in the sense… …
2Complex projective space — The Riemann sphere, the one dimensional complex projective space, i.e. the complex projective line. In mathematics, complex projective space is the projective space with respect to the field of complex numbers. By analogy, whereas the points of a …
3Blowing up — This article is about the mathematical concept of blowing up. For information about the physical/chemical process, see Explosion. For other uses of Blow up , see Blow up (disambiguation). Blowup of the affine plane. In mathematics, blowing up or… …
4Stein manifold — In mathematics, a Stein manifold in the theory of several complex variables and complex manifolds is a complex submanifold of the vector space of n complex dimensions. The name is for Karl Stein. Definition A complex manifold X of complex… …
5Calibrated geometry — In the mathematical field of differential geometry, a calibrated geometry is a Riemannian manifold ( M , g ) of dimension n equipped with a differential p form phi; (for some 0 ≤ p ≤ n ) which is a calibration in the sense that * phi; is closed:… …
6Hodge conjecture — The Hodge conjecture is a major unsolved problem in algebraic geometry which relates the algebraic topology of a non singular complex algebraic variety and the subvarieties of that variety. More specifically, the conjecture says that certain de… …
7Kähler manifold — In mathematics, a Kähler manifold is a manifold with unitary structure (a U ( n ) structure) satisfying an integrability condition.In particular, it is a complex manifold, a Riemannian manifold, and a symplectic manifold, with these three… …
8Projective space — In mathematics a projective space is a set of elements constructed from a vector space such that a distinct element of the projective space consists of all non zero vectors which are equal up to a multiplication by a non zero scalar. A formal… …
9Andreotti–Frankel theorem — In mathematics, the Andreotti–Frankel theorem states that if V is a smooth affine variety of complex dimension n or, more generally, if V is any Stein manifold of dimension n, then in fact V is homotopy equivalent to a CW complex of real… …
10Cartan's theorems A and B — In mathematics, Cartan s theorems A and B are two results proved by Henri Cartan around 1951, concerning a coherent sheaf F on a Stein manifold X . They are significant both as applied to several complex variables, and in the general development… …
