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Degree of a finite morphism $f: X\to \mathbb P^1$ induced from a non-constant rational function in the Riemann-Roch space of a divisor

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#algebraic-geometry #algebraic-curves #divisors-algebraic-geometry #projective-varieties
257
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Smooth projective surface whose hyperplane sections are elliptic curves is ruled

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#algebraic-geometry #divisors-algebraic-geometry
95
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Pencil and holomorphic map $M\setminus B\to\mathbb{P}^1$

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#algebraic-geometry #complex-geometry #divisors-algebraic-geometry
92
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Definition of singular point of a divisor

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#algebraic-geometry #complex-geometry #divisors-algebraic-geometry
81
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Very ample complete linear systems on real curves

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#sheaf-theory #algebraic-curves #projective-space #divisors-algebraic-geometry
119
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Basis of $L(4p_0)$ for a torus and induced embedding into $\mathbb{P}^3$

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#algebraic-geometry #complex-geometry #riemann-surfaces #divisors-algebraic-geometry #meromorphic-functions
840
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When does the Picard group embeds inside the divisor class group?

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#algebraic-geometry #schemes #divisors-algebraic-geometry #line-bundles
119
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Complete local domain + $(R_1)$+ depth $2$+ dimension $3$+ $Cl(R)=0 \implies$ normal (hence UFD)?

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#algebraic-geometry #commutative-algebra #homological-algebra #divisors-algebraic-geometry
176
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Divisor class group of $2$-dimensional surface isolated singularity

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#algebraic-geometry #commutative-algebra #divisors-algebraic-geometry #cohen-macaulay
78
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Local class group and Class group of localizations

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#commutative-algebra #divisors-algebraic-geometry #line-bundles
91
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Divisor class group of $2$-dimensional excellent, local normal rational singularity

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#algebraic-geometry #commutative-algebra #divisors-algebraic-geometry #cohen-macaulay
133
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Decomposition of a locally free sheaf as tensor product of sheaves

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#algebraic-geometry #complex-geometry #surfaces #divisors-algebraic-geometry
361
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Exact sequence given effective divisor

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#algebraic-geometry #sheaf-theory #schemes #divisors-algebraic-geometry
632
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Elements of the Picard group on elliptic curves

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#elliptic-curves #divisors-algebraic-geometry
35
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What is the connection between divisors and line bundles?

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#algebraic-geometry #algebraic-curves #divisors-algebraic-geometry #line-bundles

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