New posts in complex-manifolds

Identification of the holomorphic tangent space with the real tangent space

complex-geometry tangent-spaces complex-manifolds almost-complex

Understanding why nonsingular complex algebraic varieties are analytic manifolds.

algebraic-geometry complex-manifolds

Are complex projective spaces orientable?

differential-topology projective-space complex-manifolds

Why restrict to complex Lie algebras?

manifolds lie-groups lie-algebras complex-manifolds

Does every non-compact Riemann surface embed holomorphically into $\mathbb{C}^2$?

complex-analysis algebraic-geometry several-complex-variables complex-manifolds

An unclear sentence in the book "Griffiths, Harris-Principles of algebraic geometry"

differential-geometry vector-bundles curvature connections complex-manifolds

Is the homology class of a compact complex submanifold non-trivial?

algebraic-topology homology-cohomology complex-geometry complex-manifolds

Existence of $f\colon U\to V$ holomorphic non constant

complex-analysis several-complex-variables complex-manifolds

Complex and Kähler-manifolds

reference-request differential-geometry kahler-manifolds string-theory complex-manifolds

When exactly is a compact complex manifold algebraic?

algebraic-geometry complex-geometry complex-manifolds

Complex manifold with subvarieties but no submanifolds

algebraic-geometry complex-geometry complex-manifolds

Is the connected sum of complex manifolds also complex?

manifolds differential-topology complex-manifolds

(Anti-) Holomorphic significance?

complex-analysis manifolds complex-geometry complex-manifolds holomorphic-bundles

Which complex manifolds admit a collection of compatible 'charts' $\varphi_{\alpha} : U_{\alpha} \to \mathbb{C}^n$ which cover $X$?

complex-geometry complex-manifolds

Is there a complex surface into which every Riemann surface embeds?

algebraic-geometry complex-geometry riemann-surfaces complex-manifolds

Almost complex manifolds are orientable

differential-geometry complex-geometry complex-manifolds

Set of branch points isn't discrete, but branch points are isolated?

complex-analysis complex-geometry riemann-surfaces complex-manifolds branch-points

Chern classes and sums of line bundles

algebraic-geometry characteristic-classes complex-manifolds