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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
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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 …
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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 …
Niels's user avatar
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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 …
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