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Do torsion-free $\mathcal{O}_X$-modules on curves have dimension one?

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#algebraic-geometry #schemes #coherent-sheaves #projective-schemes
156
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Adjunction isomorphism in algebraic geometry

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#algebraic-geometry #algebraic-curves #schemes #coherent-sheaves
230
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What is a bilinear map of $O_X$ modules?

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#algebraic-geometry #coherent-sheaves
328
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Splitting of $f_*\mathcal O_X$

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#algebraic-geometry #schemes #coherent-sheaves
339
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Semi-stable locally free sheaves on a curve of constant slope form an abelian category

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#abstract-algebra #algebraic-geometry #sheaf-theory #vector-bundles #coherent-sheaves
155
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On a cyclic cover of genus 5 of a curve of genus 1

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#algebraic-geometry #algebraic-curves #coherent-sheaves
93
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On the support of sheaf of modules or quasi-coherent sheaves over ringed spaces

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#commutative-algebra #sheaf-theory #schemes #coherent-sheaves #quasicoherent-sheaves
273
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Direct image of coherent analytic sheaves

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#algebraic-geometry #sheaf-theory #coherent-sheaves
112
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degrees of line bundles over $y^2 = x^3 + 1$

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#algebraic-geometry #vector-bundles #coherent-sheaves
1.3k
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Reference for sheaf theory

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#sheaf-theory #sheaf-cohomology #coherent-sheaves
309
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Computing the Grothendieck group of a polynomial ring (over a field) or affine n-space as a scheme?

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#algebraic-geometry #homological-algebra #projective-module #coherent-sheaves #free-modules
166
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Why is normality of a scheme required to define the sheaf $\mathcal{L}(D)$ of a divisor?

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#algebraic-geometry #sheaf-theory #coherent-sheaves #divisors-algebraic-geometry
1k
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Definition of a Sheaf, making sense of

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#abstract-algebra #algebraic-geometry #sheaf-theory #sheaf-cohomology #coherent-sheaves
586
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morphisms to the skyscraper sheaf

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#algebraic-geometry #sheaf-theory #coherent-sheaves
1.6k
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Freeness of stalk Implies locally free

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#commutative-algebra #coherent-sheaves

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