Question

Let $M_k=\{A:rank~A\le k\}\subset Mat_{m\times n}(K)$ and $S_k=\{A:rank~A=k\}\subset Mat_{m\times n}(K)$. Show that $\bar S_k=M_k$

score 55 · Answer 1 · 2018-11-13 20:33:36

Let $M_k=\{A:rank~A\le k\}\subset Mat_{m\times n}(K)$ and $S_k=\{A:rank~A=k\}\subset Mat_{m\times n}(K)$. Show that $\bar S_k=M_k$

score 548 · Answer 2 · 2018-11-13 22:04:59

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List Question

Let $M_k=\{A:rank~A\le k\}\subset Mat_{m\times n}(K)$ and $S_k=\{A:rank~A=k\}\subset Mat_{m\times n}(K)$. Show that $\bar S_k=M_k$

Pushforward of constant sheaf on the generic point.

Unique Partition of $\{1, \dotsc, n\}$ by Ultrametric Property

Choice free method to define immersions into Projective Space

Is the Zariski topology on a variety $V$ a maximal Noetherian topology?

An example of morphism not of finite type

Constructing a local non-Noetherian domain with spectrum $\{(0), \mathfrak{m} \}$.

Counting rational points

Sheaves of abelian groups and tensor product

Question about a proof for extending a local homomorphism to a morphism of schemes

Zero-dimensional Hilbert scheme of two points and Hilbert-Chow morphism

Is it possible to define schemes without using sheaves?

Closed embedding in flat topology

Let $f$ be a real irreducible hypersurface of $\mathbb R^n$. Is $I(V(f))=(f)\subset\mathbb R[x_1,\dots, x_n]$?

Construction of surfaces with Kodaira dimension 1

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