List questions from affine-varieties

Published on 07 May 2023 - 4:07

57

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$X\times Y$ and the product topology

Published on 25 Mar 2026 - 23:33

135

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Irreducible components, dimension and degree of projective varieties

Published on 09 May 2023 - 5:26

86

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Checking smoothness of curves and finding multiplicites.

Published on 09 May 2023 - 6:26

85

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Show that $\mathcal{I}(\bigcup_iX_i)=\bigcap_i\mathcal{I}(X_i)$.

Published on 13 May 2023 - 6:36

108

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Trouble understanding Hartshorne's Algebraic Geometry Exercise 2.2 (Chapter 1).

Published on 25 Mar 2026 - 20:34

136

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Show that the equation of conic in $\mathbb{P}^2$ can we written as $ax^2+by^2+cz^2=0$.

Published on 17 May 2023 - 10:11

154

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Is a morphism of varieties determined by its behaviour on an open subset

Published on 25 Mar 2026 - 23:37

54

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Is every affine variety an affine scheme?

Published on 29 May 2023 - 11:44

121

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Does the completions $\hat{\mathscr{O}}_P(X)\simeq \hat{\mathscr{O}}_Q(Y)$ could deduce local rings $\mathscr{O}_P(X)\simeq \mathscr{O}_Q(Y)$?

Published on 25 Mar 2026 - 23:42

13

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Is left t-exactness of $Rf_\ast$ for $f : X\longrightarrow Y$ affine just Andreotti-Frenkel

Published on 17 Jun 2023 - 17:28

103

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Finding $I(V)$ for $V = V(x^2 + y^2 - z^2, 2z^2 - y)$

Published on 22 Jun 2023 - 6:02

29

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Dimension of open subset of affine variety

Published on 29 Jun 2023 - 23:37

171

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Geometrical interpretation of $\operatorname{Spec}(\mathbb{R}[x,y]/(x^2+y^2))$

Published on 05 Jul 2023 - 13:12

32

Views

Confusion about the definition of local ring of an affine variety at a point and its relation with localization

Published on 28 Jul 2023 - 7:36

List Question

Birational morphism of the affine line

$X\times Y$ and the product topology

Irreducible components, dimension and degree of projective varieties

Checking smoothness of curves and finding multiplicites.

Show that $\mathcal{I}(\bigcup_iX_i)=\bigcap_i\mathcal{I}(X_i)$.

Trouble understanding Hartshorne's Algebraic Geometry Exercise 2.2 (Chapter 1).

Show that the equation of conic in $\mathbb{P}^2$ can we written as $ax^2+by^2+cz^2=0$.

Is a morphism of varieties determined by its behaviour on an open subset

Is every affine variety an affine scheme?

Does the completions $\hat{\mathscr{O}}_P(X)\simeq \hat{\mathscr{O}}_Q(Y)$ could deduce local rings $\mathscr{O}_P(X)\simeq \mathscr{O}_Q(Y)$?

Is left t-exactness of $Rf_\ast$ for $f : X\longrightarrow Y$ affine just Andreotti-Frenkel

Finding $I(V)$ for $V = V(x^2 + y^2 - z^2, 2z^2 - y)$

Dimension of open subset of affine variety

Geometrical interpretation of $\operatorname{Spec}(\mathbb{R}[x,y]/(x^2+y^2))$

Confusion about the definition of local ring of an affine variety at a point and its relation with localization

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