List questions from affine-varieties

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Morphism from complete variety to an affine variety

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An introductory book on varieties and smooth algebraic curves?

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149

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Are the affine and projective spaces $k^n$ and $P^n(k)$ , homeomorphic w.r.t. to the Zariski topology on them?

Published on 23 Apr 2026 - 7:12

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For which $m,n$, are the affine spaces $\mathbb A^n(k)$ and $\mathbb A^m(k)$ , with Zariski topology, are homeomorphic?

Published on 23 Apr 2026 - 9:54

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Under Zariski topology , $ \operatorname{Spec} k[X,Y] \cong \operatorname{Spec} k[X] \times \operatorname{Spec}k[Y]$?

Published on 23 Apr 2026 - 13:22

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Complement of a Conic is Affine

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When is a variety defined by two quadratics irreducible?

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405

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There Exist Exactly Two Nonisomorphic Affine Conic Plane Curves

Published on 15 Apr 2026 - 20:20

57

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Some basic definitions on algebraic geometry

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$V(I(X)) \cap V(I(Y)) = \emptyset \Leftrightarrow\exists f \in K[x_1,...,x_n] : f(x)=0 \forall x \in X \text { and } f(x)=1 \forall x \in Y$

Published on 16 Apr 2026 - 4:46

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Formal Definition of Algebraic Variety

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Equivalent definition of regular map between quasi-projective varieties.

Published on 15 Apr 2026 - 23:06

51

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Question about implization theorem and Gröbner basis

Published on 14 Apr 2026 - 18:26

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Is $X=(x^2-yx, y^2-xz, z^2-x^2y) $ isomorphic to $ \mathbb A_{K}^1$?

Published on 15 Apr 2026 - 4:43

List Question

Parametrize a Variety in Projective Space

Morphism from complete variety to an affine variety

An introductory book on varieties and smooth algebraic curves?

Are the affine and projective spaces $k^n$ and $P^n(k)$ , homeomorphic w.r.t. to the Zariski topology on them?

For which $m,n$, are the affine spaces $\mathbb A^n(k)$ and $\mathbb A^m(k)$ , with Zariski topology, are homeomorphic?

Under Zariski topology , $ \operatorname{Spec} k[X,Y] \cong \operatorname{Spec} k[X] \times \operatorname{Spec}k[Y]$?

Complement of a Conic is Affine

When is a variety defined by two quadratics irreducible?

There Exist Exactly Two Nonisomorphic Affine Conic Plane Curves

Some basic definitions on algebraic geometry

$V(I(X)) \cap V(I(Y)) = \emptyset \Leftrightarrow\exists f \in K[x_1,...,x_n] : f(x)=0 \forall x \in X \text { and } f(x)=1 \forall x \in Y$

Formal Definition of Algebraic Variety

Equivalent definition of regular map between quasi-projective varieties.

Question about implization theorem and Gröbner basis

Is $X=(x^2-yx, y^2-xz, z^2-x^2y) $ isomorphic to $ \mathbb A_{K}^1$?

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