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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.

2 votes
0 answers
199 views

Direct proof that Brody hyperbolic implies algebraically hyperbolic

Setup. Let $X$ be a compact complex manifold. Let $\sum\limits \omega_{jk}d{z_j}\otimes d\overline{z}_k$ be a Hermitian metric on $X$ with associated positive $(1,1)$-form $\omega = \frac{i}{2}\sum \o …
7 votes
1 answer
324 views

Indeterminacy locus of meromorphic maps of rigid analytic spaces

Setup. Let $k$ be an algebraically closed field of characteristic zero. Let $X/k$ be a normal variety, and let $Y/k$ be a proper variety. It is well-known that the indeterminacy locus of a rational ma …
2 votes

Indeterminacy locus of meromorphic maps of rigid analytic spaces

Since this answer might be of use to other people in the future, I wanted to add an answer to this question. Brian Conrad provided me with a proof of this fact, which is written up Section 3 of arXiv …
Jackson Morrow's user avatar