**11**

votes

**0**answers

149 views

### Entropy in elimination theory, or a brief remark by Gelfand-Kapranov-Zelevinsky

In the introduction to their book "Discriminants, resultants and multidimensional determinant", the authors state a very intriguing observation concerning the coefficients of monomials appearing in ...

**8**

votes

**1**answer

950 views

### Why A. Weil considered elimination theory to be eliminated?

It is well known that AndrĂ© Weil declared, in the 1940's, that elimination theory must be eliminated from algebraic geometry. I would like to understand his mathematical reasons to adopt such an ...

**-2**

votes

**1**answer

286 views

### Why is any maximal minor of the Bezoutian matrix divisible by the resultant?

I'm referring to Emiris and Mourrain's paper "Matrices in Elimination Theory," Theorem 3.13. Toward the end of the proof, it says that, just because $(f_1,\ldots,f_{n+1})$ is dense in ${\cal Z}({\rm ...

**1**

vote

**1**answer

210 views

### Calculating the images of varieties under projections

Dear all,
I am interested in the following basic and fundamental question in elimination theory: given a variety in some product space $Z\subseteq X\times Y$, how could I explicitly calculate the ...

**1**

vote

**5**answers

295 views

### Interpolating for particular coefficients

Say $F(X) \in \mathbb{Z}[X]$ is an even degree polynomial of degree $2n$.
One needs to evaluate $F(X)$ at $O(n)$ points to interpolate and get all the coefficients of $F(X)$.
However say I need ...

**2**

votes

**3**answers

853 views

### General hyperplane sections and projection from a point

Let $k$ be an algebraically closed field, and consider some subscheme $X\subset \mathbb{P}_k^n$. Let $x$ be a closed point of $X$, and $H$ a general hyperplane containing $x$. There is a regular map ...

**5**

votes

**1**answer

2k views

### Polynomial with two repeated roots

I have a polynomial of degree 4 $f(t) \in \mathbb{C}[t]$, and I'd like to know when it has two repeated roots, in terms of its coefficients.
Phrased otherwise I'd like to find the equations of the ...