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What's an $\mathcal O_X$-algebra when $X= \operatorname{Spec} R$?

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#algebraic-geometry #schemes #affine-schemes
173
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Sheaves on a scheme compared with sheaves on its étale site

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#algebraic-geometry #schemes
563
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Cohomology group of the affine plane without origin: need help with algebraic computation

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#algebraic-geometry #commutative-algebra #sheaf-cohomology
256
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Exercise 2.2.5 in Qing Liu's book

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#algebraic-geometry
181
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Is there a converse of Abhyankar-Moh-Suzuki theorem?

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#algebraic-geometry #polynomials #commutative-algebra #field-theory
238
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Every affine variety is birational to its projective closure ?

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#algebraic-geometry #commutative-algebra
52
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$F(U)=\{ f \in \mathbb{C}(U) \mid z \dfrac{df}{dz}=1 \}$. Show that $F$ is a sheaf and determine its stalks.

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#algebraic-geometry
304
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Realizing subring as ring of invariants?

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#abstract-algebra #algebraic-geometry #commutative-algebra #invariant-theory
461
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Fibre product of projective schemes over an affine scheme

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#abstract-algebra #algebraic-geometry
602
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Proof of Serre Duality in Hartshorne

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#algebraic-geometry #homology-cohomology #sheaf-cohomology
253
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Almost all singular hypersurfaces are reducible?

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#algebraic-geometry #complex-geometry
699
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Algebraic differential form

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#algebraic-geometry #commutative-algebra #differential-forms
137
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A naive question about the scheme theory: regard $\mathbb C^n$ as a scheme

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#algebraic-geometry #soft-question #schemes #affine-schemes
3.9k
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The twisting sheaf

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#algebraic-geometry #sheaf-theory #schemes
196
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General singular cubic surface consists of $6$ lines of multiplicity two and $15$ single lines?

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#algebraic-geometry

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