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Results tagged with complex-geometry
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user 131975
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.
11
votes
1
answer
526
views
What is a "non-trivial" example of a commutative algebraic group over $\mathbb{C}$?
Let $G$ be a commutative connected algebraic group over $\mathbb{C}$. A theorem of Serre says that there exists an exact sequence
$$1\to \mathbb{G}_a^n\times \mathbb{G}_m^m\to G\to A\to 1,$$
where $A$ …
- 773
25
votes
0
answers
2k
views
Is there a proof of Hodge theory using condensed mathematics?
As is well known, many results in complex geometry "feel" algebraic (and often have statements which are "completely algebraic") but only have "transcendental" proofs (i.e., using analysis in some ess …
- 773
5
votes
1
answer
306
views
$\ell$-adic analogue of Kedlaya–Mochizuki
There is a well-known analogy between holonomic $\mathcal{D}$-modules on complex algebraic varieties and $\ell$-adic perverse sheaves on varieties over finite fields. Many theorems in one setting have …
- 773