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Holomorphic functions on Riemann surfaces with boundary

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#riemannian-geometry #riemann-surfaces #complex-manifolds
58
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lower bound the distance between two varieties

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#algebraic-geometry #numerical-methods #smooth-manifolds #computer-algebra-systems #complex-manifolds
294
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Every closed orientable surface is Riemann surface

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#manifolds #surfaces #riemann-surfaces #complex-manifolds
261
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Fundamental form of almost complex manifold is $(1,1)$-form

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#differential-forms #complex-geometry #complex-manifolds #tangent-spaces #almost-complex
54
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Del-bar commuting with averaging operator

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#lie-groups #group-actions #complex-manifolds
400
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the simplest non-trivial line bundle over Riemann sphere

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#vector-bundles #riemann-surfaces #fiber-bundles #complex-manifolds
22
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Are the two parts of a Hermitian metric compatible in the Levi-Civita sense?

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#metric-spaces #vector-bundles #complex-manifolds
150
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Product of two Riemann surfaces $X$ with $H^1(X,T_X)<H^2(X,\mathcal{O})$

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#algebraic-geometry #complex-geometry #riemann-surfaces #complex-manifolds #deformation-theory
103
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Riemann-Roch theorem for minimal Kähler surface.

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#algebraic-geometry #complex-geometry #kahler-manifolds #complex-manifolds
155
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Reference on learning Donaldson's construction on sections

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#complex-geometry #symplectic-geometry #fibration #complex-manifolds #contact-topology
3.1k
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Are complex projective spaces orientable?

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#differential-topology #projective-space #complex-manifolds
2.5k
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Volume form on a complex manifold vs. volume form on the underlying real manifold

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#differential-forms #complex-geometry #complex-manifolds
484
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Complex structure on $\mathbb S^1 \times \mathbb S^3$

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#complex-geometry #complex-manifolds
112
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How do you construct proofs for complex manifolds that in the real case need of partitions of unity?

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#smooth-manifolds #holomorphic-functions #complex-manifolds
87
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Hermitian invertible sheaf on a Riemann surface.

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#algebraic-geometry #sheaf-theory #riemann-surfaces #complex-manifolds

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