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Complex geometry is the study of complex manifolds, complex algebraic varieties, complex analytic spaces, and, by extension, of almost complex structures. It is a part of differential geometry, algebraic geometry and analytic geometry.

5 votes

Monge Ampere equations

Though it doesn't focus exclusively on complex Monge-Ampere equations, I learnt a lot from Gilbarg and Trudinger's book "Elliptic pdes of second order".
Hwasung Lee's user avatar
10 votes
1 answer
1k views

When is a holomorphic tangent bundle stable?

Hello, I was thinking about the stability condition in terms of Mumford and I have a question: If $S$ is a compact Kahler surface (complex 2D), when is the holomorphic tangent bundle $T^{1,0}S$ stab …
Hwasung Lee's user avatar