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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.
18
votes
Accepted
What are parabolic bundles good for?
Parabolic bundles were introduced in the 70's by Mehta and Seshadri in the set
up of a Riemann surface with cusps. They were trying to generalize the
Narasimhan-Seshadri correspondence on a compact Ri …
5
votes
Non-Abelian Hodge theory
I recently attented a nice online talk by Pengfei Huang and he indicated two sources:
the first chapter of his own phd Non-abelian Hodge theory and some specializations - TEL - Thèses en ligne
Intro …
4
votes
Finite etale atlas for Deligne-Mumford stacks
To give a more simple example than Daniel's, you can just consider for X a projective line with a single orbifold point. By Riemann-Hurwitz X is simply connected and so there is no non-trivial finite …