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15
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Direct proof for $\mathcal{O}_{\mathbb{CP}_{1}}(-2) \cong T^{*}\mathbb{CP}_{1}$

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#complex-geometry #holomorphic-bundles #line-bundles
192
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Hermitian holomorphic Connection and Dolbeault operator

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#differential-geometry #kahler-manifolds #hodge-theory #holomorphic-bundles
317
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A complex vector bundle $E$ is a holomorphic vector bundle iff $(\overline{\partial^E})^2=0$ help with proof?

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#differential-geometry #complex-geometry #vector-bundles #holomorphic-bundles #almost-complex
112
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Cyclic vector of local system

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#ordinary-differential-equations #holomorphic-bundles #d-modules
47
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Orthogonality and Chern classes in holomorphic bundles over the Riemann sphere

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#differential-geometry #complex-geometry #holomorphic-bundles
159
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Why is $\int_M i \partial\bar \partial u \wedge \Phi^{n-1}$ zero?

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#differential-geometry #complex-geometry #vector-bundles #kahler-manifolds #holomorphic-bundles
1.3k
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Fubini Study metric on the complex projective space $\mathbb{PC}^m$

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#differential-geometry #complex-geometry #kahler-manifolds #holomorphic-bundles
188
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Basic question: Curvature transforms under Complexified Gauge Transformation

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#differential-geometry #reference-request #riemann-surfaces #gauge-theory #holomorphic-bundles
1.1k
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Holomorphic vector bundles on almost complex manifolds

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#complex-geometry #kahler-manifolds #holomorphic-bundles #almost-complex
2.1k
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If a holomorphic bundle is smoothly trivial, is it holomorphically trivial?

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#differential-geometry #complex-geometry #holomorphic-bundles
563
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Atiyah Bundles over Elliptic Curves

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#algebraic-geometry #elliptic-curves #complex-geometry #holomorphic-bundles
594
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Adjunction formula for sub varieties of $\mathbb{P}^n$

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#algebraic-geometry #complex-geometry #holomorphic-bundles
102
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What is the difference between $\mathcal{O}_X$ and $\mathcal{O}_X(n)$?

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#algebraic-geometry #sheaf-theory #vector-bundles #fiber-bundles #holomorphic-bundles
71
Views

Abel Jacobi Theorem from sheaf theory

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#complex-geometry #sheaf-cohomology #holomorphic-bundles
886
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Confusion about Positive Curvature in Holomorphic Bundles.

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#differential-geometry #algebraic-geometry #complex-geometry #vector-bundles #holomorphic-bundles

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