# Questions tagged [determinantal-ideals]

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7
questions

**9**

votes

**2**answers

256 views

### Can we recover all $k$-minors of a square matrix from some of them?

This is a cross-post.
Let $k,n$ be natural numbers, $1<k<n$. Suppose we have an "unknown" invertible $n \times n$ matrix $A$ over a field of characteristic zero. (we do not know the entries of ...

**2**

votes

**1**answer

175 views

### what are the possible approximations for ideals

(Fix some local ring $(R,\mathfrak{m})$ over a field of zero characteristic.)
Suppose an ideal $J$ is defined by some complicated formula/procedure. And there is no hope of computing it/or writing ...

**4**

votes

**3**answers

555 views

### Equations for points to lie on a rational normal curve

$\def\PP{\mathbb{P}}$Let $z_1$, $z_2$, ..., $z_n$ be points in $\PP^{k-1}$. I am interested in equations for when the $z_i$ lie on a rational normal curve (or degeneration thereof.)
Specifically, ...

**5**

votes

**1**answer

1k views

### Vanishing patterns of minors of matrix

Let $M$ be a $m\times n$ matrix with entries in, say $\mathbb{C}$; assume $n\leq m$. Denote by $I\subseteq\{1,2,\ldots, n\}$ a subset of the columns of M. I am interested in positive results to the ...

**2**

votes

**1**answer

163 views

### minimality/universality of the Springer resolution of a determinantal variety

Let $X\subset P^n$ be a singular determinantal variety and $S\to X$ its Springer resolution. Let $X'\to X$ another resolution of singularities (say, a blow-up). Does $S$ have some minimality/...

**1**

vote

**3**answers

523 views

### Syzygies of determinantal varieties: Looking for English text

I would like to understand the syzygies of the determinantal ideal $I_r$, generated by the $r\times r$ minors of a matrix $(X_{ij})$ of indeterminantes in the polynomial ring over an algebraically ...

**8**

votes

**1**answer

275 views

### When two determinantal ideals together generate a power of the maximal ideal?

(A somewhat technical question, but maybe it is well known.)
Consider matrices over the ring $k[[x_1,\dots,x_n]]$, whose entries vanish at the origin (i.e. belong to the maximal ideal $\mathfrak{m}$...