Prove the dimension of an affine algebraic variety X is equal to the dimension of its projective closure $\overline{X}$
47537
Open nonempty subset of irreducible variety over $k$ has the same Krull dimension as the whole variety?
142097
Finding the dimension of the orthogonal complement
55488
Proving that $\operatorname{codim}(X,Y)=\dim(\mathcal{O}_{X,\eta})$
103136
Geometric intuition of the dimension of Grassmannians and flag manfolds
107281
Proof of Existence of Algebraic Closure: Too simple to be true?
17404
Artinian affine $K$-algebra
53432
What is the algebraic closure of $\mathbb F_q$?
129184
Krull dimension of this local ring
145039
Algebraic independence over $\overline{\mathbb Q}$ and over $\mathbb Q$
100340
Invariant dimension property on a ring without zero divisors
75829
Dimension of open subsets of $R^n$
81550
Linking two theorems: on algebraic closure and on minimal splitting field
157109
Finding the Dimension of a Matrix Polynomial: $W$ = { $p(B)$ : $p$ is a polynomial with real coefficients}
34693
Prove $E^{\mathbb Q}[Y]=E^{\mathbb P}[XY]$ if $E^{\mathbb P}[X]=\mathbb P(X>0)=1$ and $ \mathbb Q(A)=E^{\mathbb Q}[X1_A] $
51790
Krull Dimension of a scheme
47266
Every affine variety in $\mathbb A^n$ consisting of finitely many points can be written as the zero locus of $n$ polynomials
29653
Show that $xy=0$ is a variety but not a manifold