Complex geometry is the study of complex manifolds and complex algebraic varieties. It is a part of both differential geometry and algebraic geometry.

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### Chow theorem in $\mathbb{C}^2$

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### Differential operator of globally unbounded order on connected complex manifold?

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### Universal cover of ladderly puntured complex plane

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**0**answers

### Is Serre duality related to Pontryagin duality?

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### Is singular Cauchy operator bounded in Morrey spaces?

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### Can the base of an elliptically fibered Calabi-Yau threefold be an Enriques surface?

**5**

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### Good reduction of abelian varieties over valuation rings via coverings

**9**

**2**answers

### Do abelian varieties have Neron models over arbitrary valuation rings?

**7**

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### Explicit descriptions of a flop

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### What is the unitary $1$-parameter group generated by a vector field on a manifold?

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**1**answer

### Chain rotation of a point

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**1**answer

### Formal complex manifold without dd^c

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### What is the Jarlskog invariant, conceptually?

**7**

**4**answers

### Lattices of PU(n,1) with large abelianization

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**1**answer

### Is a smooth intersection of hypersurfaces equidimensional?

**2**

**1**answer

### Why are modular curves non-trivial covers of the $j$-line

**7**

**1**answer

### How does one complexify a real $n$-dimensional Riemannian manifold $(M,g)$?

**5**

**1**answer

### Fulton's deformation to the normal cone vs Verdier's

**6**

**2**answers

### Harder Narasimhan filtration for the endomorphism bundle

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**1**answer

### Do line bundles with enough sections on surfaces have generic divisors which are irreducible?

**3**

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### Algebrizing analytic quotients of algebraic spaces

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**1**answer

### Exponential Sequence of Sheaves

**5**

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### Asphericity of hypersurface complement in ${\mathbb C}^n$

**2**

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### Kähler manifold with a global potential

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**0**answers

### The comparison of certain modules arising from the Cauchy-Riemann differential operator

**2**

**1**answer

### Admissible global residues on smooth variety with normal crossings divisor

**2**

**1**answer

### Movable divisor with base locus on a hyperkahler variety

**5**

**0**answers

### a question on Hodge and Atiyah's paper “integrals of the second kind on an algebraic variety”

**1**

**0**answers

### Numerical equivalent positive non-degenerate divisor induced projective embedding involves Veronese map?

**5**

**0**answers

### Dimension of linear complex-symplectic reduction

**12**

**2**answers

### Algebraic vs analytic normality

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**0**answers

### Kelly's theorem for quadratic polynomials

**4**

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### Continuous function on a complex space that is holomorphic on the complement of a closed subspace

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**1**answer

### Holomorphic line bundles with torsion Chern class [closed]

**6**

**1**answer

### Rationality of the moduli space of genus g curves

**2**

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### Status of global spherical shell conjecture for minimal complex surfaces?

**0**

**1**answer

### Kähler form on complex projective algebraic variety [closed]

**2**

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### Does there exist a leaf of this holomorphic foliation with non trivial holonomy?

**5**

**2**answers

### Embedding of a complex submanifold in projective space

**2**

**1**answer

### Set of sections whose zeroes avoid a given divisor is (Zariski) dense?

**1**

**0**answers

### What separates a cyclic polytope from a projective polytope?

**6**

**1**answer

### Are there non-projective, but algebraic, hyperkahler varieties?

**6**

**1**answer

### The Ricci Form and the First Chern Class

**4**

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### Structure of the Kähler cone

**2**

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### Degeneration of a metric

**2**

**2**answers

### When is the space of holomorphic sections of the tensor product of two line bundles given by the span of the tensor product of the basis?

**1**

**0**answers

### (Real) holomorphic vector fields on compact Kähler manifolds

**3**

**2**answers

### Criteria for a coherent sheaf pushing forward from the universal cover

**4**

**1**answer

### Can an algebraic variety over a field $k$ be the union of proper closed subsets $(S_i)_{i\in I}$ with $I < k$

**4**

**1**answer