List questions from algebraic-geometry

Published on 15 Apr 2026 - 9:03

149

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$ \mathbb{A}^{1}_{k}\backslash \lbrace a_{1},\dots,a_{l} \rbrace \cong \mathbb{A}^{1}_{k}\backslash \lbrace b_{1},\dots,b_{m} \rbrace. $ Is $ l = m?$

Published on 16 Apr 2026 - 9:31

365

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What is the correct definition of the inverse image functor on sheaves of modules?

Published on 25 Mar 2026 - 19:10

117

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How general fibers determine a special fiber?

Published on 11 Apr 2026 - 18:32

91

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What shapes are "drawable" on $\mathbb R^2$ with polynomials?

Published on 11 Apr 2026 - 7:10

54

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Number of solutions $\text{mod}\;p$ for all $p$ and Betti numbers

Published on 15 Apr 2026 - 8:11

233

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Why is the Grassmannian functor representable by a scheme?

Published on 25 Mar 2026 - 7:51

52

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Basis of very ample line bundle

Published on 13 Apr 2026 - 2:18

206

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Action of the multiplicative group induced by a grading

Published on 25 Mar 2026 - 9:26

130

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Polar divisor contains no hyperplane when degree $d\geq 3$

Published on 14 Apr 2026 - 8:44

44

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What goes wrong in the proof that $Spec \mathbb{R}[x,y]/(x^2+y^2)$ is a principal divisor in $Proj \mathbb{R}[x,y,z]/(x^2+y^2+z^2)$

Published on 16 Apr 2026 - 13:23

37

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lower bounds for points of a smooth variety over finite field

Published on 13 Apr 2026 - 2:46

98

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locus of smooth points in Hilbert scheme

Published on 12 Apr 2026 - 3:39

116

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Localization in the Harsthorne definition of the spectrum of a ring

Published on 13 Apr 2026 - 15:21

60

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Showing the following subset is an affine variety

Published on 15 Apr 2026 - 5:09

List Question

Equidimensional affine ring

$ \mathbb{A}^{1}_{k}\backslash \lbrace a_{1},\dots,a_{l} \rbrace \cong \mathbb{A}^{1}_{k}\backslash \lbrace b_{1},\dots,b_{m} \rbrace. $ Is $ l = m?$

What is the correct definition of the inverse image functor on sheaves of modules?

How general fibers determine a special fiber?

What shapes are "drawable" on $\mathbb R^2$ with polynomials?

Number of solutions $\text{mod}\;p$ for all $p$ and Betti numbers

Why is the Grassmannian functor representable by a scheme?

Basis of very ample line bundle

Action of the multiplicative group induced by a grading

Polar divisor contains no hyperplane when degree $d\geq 3$

What goes wrong in the proof that $Spec \mathbb{R}[x,y]/(x^2+y^2)$ is a principal divisor in $Proj \mathbb{R}[x,y,z]/(x^2+y^2+z^2)$

lower bounds for points of a smooth variety over finite field

locus of smooth points in Hilbert scheme

Localization in the Harsthorne definition of the spectrum of a ring

Showing the following subset is an affine variety

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