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What happens when we compactify every fibre of a holomorphic $\Bbb C$ bundle over a compact Riemann surface?

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#riemann-surfaces #holomorphic-bundles
47
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Equivalent definition to holomorphic vector bundle

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#differential-geometry #complex-geometry #holomorphic-bundles
88
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Does a compact Kahler manifolds with negative first Chern class admits any nontrivial holomorphic vector field?

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#differential-geometry #complex-geometry #characteristic-classes #holomorphic-bundles
228
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Algebraic vector bundles which are analytically but not algebraically isomorphic

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#algebraic-geometry #complex-geometry #vector-bundles #holomorphic-bundles
28
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Finding a holomorphic representing section

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#differential-geometry #vector-bundles #holomorphic-bundles
41
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Lefschetz operator on bundle-valued forms

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#differential-geometry #complex-geometry #differential-forms #kahler-manifolds #holomorphic-bundles
22
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Holomorphic function of several complex variables and sets of zero Lebesgue measure

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#real-analysis #complex-analysis #lebesgue-measure #holomorphic-bundles
758
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Elements of the zero-th Čech cohomology group versus global holomorphic sections

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#algebraic-geometry #complex-geometry #vector-bundles #sheaf-cohomology #holomorphic-bundles
387
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Fano-ness of moduli space of stable vector bundles when determinant line bundle is *not* fixed...

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#algebraic-geometry #complex-geometry #holomorphic-bundles
7.3k
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Comparing notions of degree of vector bundle

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#algebraic-geometry #algebraic-topology #vector-bundles #holomorphic-bundles
335
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Comparing vector bundle degrees coming from different embeddings into projective space

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#algebraic-geometry #complex-geometry #projective-space #kahler-manifolds #holomorphic-bundles
93
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Compactness of the moduli space of bundles with fixed determinant

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#algebraic-geometry #riemann-surfaces #holomorphic-bundles
2k
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Existence of a holomorphic connection implies existence of a flat connection

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#differential-geometry #complex-geometry #vector-bundles #connections #holomorphic-bundles
242
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Line bundle of degree 1 on a genus 2 surface without global holomorphic sections

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#algebraic-geometry #riemann-surfaces #holomorphic-bundles
338
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Show this function is holomorphic

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#complex-analysis #holomorphic-bundles

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