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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.

3 votes
0 answers
49 views

Geodesics in norm balls

Recently, some problems that I work on require that I understand a bit of hyperbolic complex geometry. Assume that $B \subset \mathbb{C}^n$ is the unit ball of some norm $\|\cdot\|$ (not induced by an …
shamovic's user avatar
  • 431
2 votes
1 answer
179 views

Analytic sections of a GIT quotient lying in the Kempf-Ness set

I would like to understand whether the following is true. Given a complex reductive group $G$ (for me $G = \operatorname{PGL}_n(\mathbb{C})$) acting on a vector space $V$ (for me $V = M_n(\mathbb{C})^ …
shamovic's user avatar
  • 431
1 vote
0 answers
98 views

Holomorphic line bundles on smooth points of a quotient

I am an amateur algebraic geometer, so maybe this question is trivial and if this is the case, then I apologize. This is a question that came up while working on something completely different. Consi …
shamovic's user avatar
  • 431