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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
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 …
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 …