7
votes
Accepted
Can we recover all $k$-minors of a square matrix from some of them?
It depends how you frame the question, but the answer is yes in some sense. Let $A$ be the $n \times n$ generic matrix with linear entries in $\mathbb{k}[x_1, \ldots, x_{n^2}]$. I denote by $I_m$ the ...
- 7,300
4
votes
Equations for points to lie on a rational normal curve
I would like to suggest the following paper, where my coauthors and I try to give a partial answer to this question
https://arxiv.org/abs/1711.06286
Roughly speaking, the idea is to use the Gale ...
- 411
3
votes
Accepted
What is the relationship between determinantal varieties?
Set $M_k:=V(I_k) \subset \operatorname{Mat}(m \times n) \simeq \mathbb{A}^{mn}$.
(1) If $k < \min\{m, \, n\}$ then $M_{k-1}$ is precisely the singular locus of $M_k$. See
E. Arbarello, M. Cornalba,...
- 66.3k
3
votes
Accepted
"Classical" proof that maximal minors form a Grobner basis under diagonal term order
Here are a few articles that might be relevant:
Narasimhan, The irreducibility of ladder determinantal varieties, from 1986. It takes about 20 pages to prove the result (that the minors are a standard ...
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3
votes
Can we recover all $k$-minors of a square matrix from some of them?
Here is another point of view on the question.
Assume that you are interested in $k$-minors, what you're going to do is focus on submatrices of $A$ of size $k\times n$ by eliminating $n-k$ rows. Such ...
- 1,005
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