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Results tagged with complex-geometry
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user 6074
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.
21
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0
answers
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Cartan–Oka vanishing in one variable without $\overline{\partial}$?
This is a literature question, about possible proofs of some very basic results in complex analysis.
Some key facts about holomorphic functions are proved via reduction to smooth functions, using $\ov …
- 21.3k
12
votes
1
answer
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Accumulation of algebraic subvarieties: Near one subvariety there are many others (?), 2
This is a sequel to the question Accumulation of algebraic subvarieties: Near one subvariety there are many others (?) .
Let $Y$ be some projective variety, over $\mathbb{C}$. Let $X\subset Y$ be som …
- 21.3k
12
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Mixing solids and liquids
Good question!
I think the real context for the question was whether certain objects that are implicit in work of Darmon (and collaborators) could exist within this framework of analytic geometry. The …
- 21.3k
27
votes
2
answers
3k
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Accumulation of algebraic subvarieties: Near one subvariety there are many others (?)
Let's work over the field $\mathbb{C}$ of complex numbers, and let $X\subset \mathbb{P}^n$ be a projective variety. Let $\tilde{X}\subset \mathbb{P}^n$ be any small open neighborhood of $X$, in the co …
- 21.3k
19
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1
answer
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Accumulation of algebraic subvarieties: Near one subvariety there are many others (?), 3
Part 3 of this series of questions. In the meantime, I realized that there is some very simple question that was left open in Accumulation of algebraic subvarieties: Near one subvariety there are many …
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11
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Accumulation of algebraic subvarieties: Near one subvariety there are many others (?), 3
The answer to the question for general $X$ is no: There are local obstructions coming from bad singularities.
More precisely, one can show the following: Assume that $X$ is irreducible and that there …
- 21.3k