List questions from affine-varieties

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Base change of a homeomorphism of varieties

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Cover an affine variety by finitely many disjoint irreducible affine subvarieties

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Let $X \subseteq Y$ are affine varieties. If $X$ is irreducible then $X$ is contained in an irreducible component of $Y$.

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Zariski closure of a set in $k^3$

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Zero set of analytic function of two-variables smooth

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Localization of the coordinate ring $K[V]$, $K$ not necessarily algebraically closed.

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$p\circ h\in I(X)$ if and only if $p\in I(\overline{h(X)})$?

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Fiber product of two affine varieties

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Computation of the maximal ideal of a localized quotient ring

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An element from a coordinate ring inducing a function

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Regular functions on the complement of an irreducible conic in $\mathbb{P}^2$

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What does the word $ \ \text{affine} \ $ impose in mathematics?

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List Question

Find irreducible components of $V(y − x^2, y^2 − y + z^2)$

Base change of a homeomorphism of varieties

Cover an affine variety by finitely many disjoint irreducible affine subvarieties

Let $X \subseteq Y$ are affine varieties. If $X$ is irreducible then $X$ is contained in an irreducible component of $Y$.

Zariski closure of a set in $k^3$

Zero set of analytic function of two-variables smooth

Localization of the coordinate ring $K[V]$, $K$ not necessarily algebraically closed.

$p\circ h\in I(X)$ if and only if $p\in I(\overline{h(X)})$?

Fiber product of two affine varieties

Computation of the maximal ideal of a localized quotient ring

Isomorphic as affine schemes v.s. isomorphic as affine $k$-schemes

Understanding Hartshorne's definition of subvariety

An element from a coordinate ring inducing a function

Regular functions on the complement of an irreducible conic in $\mathbb{P}^2$

What does the word $ \ \text{affine} \ $ impose in mathematics?

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