Almost complex manifolds are orientable

Here’s a slightly different way of looking at it. First, note that we can choose a Riemannian metric \$g\$ on …

All Kähler metrics on a complex manifold?

adding my comment as an answer In general, Kahler metrics in \$[ω_0]\$ can also be parametrised as metrics of the …

Algebraic vs analytic normality

Over \$mathbf{C}\$, algebraic normalization and analytic normalization are equivalent concepts. See N. Kuhlmann: Die Normalisierung komplexer Räume, Math. Ann. 144 …

Algebraic de Rham cohomology vs. analytic de Rham cohomology

If \$X\$ is smooth and proper, GAGA does in fact suffice (despite the observation that \$d\$ is not \$mathcal{O}_X\$-linear: One …

A harmonic function

Yes, it can be found explicitly, though not in elementary functions but in terms of a combination of elementary and …

A geometric definition of the addition law on abelian surfaces

This must be standard, I don’t have a reference but the construction is easy: let \$y^2=f(x)\$ be a genus 2 …

Adjunction formula (Griffiths & Harris proof)

The normal bundle Choose on each \$U_i\$ a coordinate system \$(z_1^{i},…,z_n^{i})\$ such that \$U_icap V\$ is given by the equation …