a syzygy is a relation between the generators of a module M.

**2**

votes

**1**answer

346 views

### Castelnuovo Mumford Regularity

Consider the polynomial ring $S = C[x_1,\ldots,x_n]$. Let
$$
0 \rightarrow E_{n-1} \rightarrow \cdots \rightarrow E_1 \rightarrow E_0 \rightarrow I \rightarrow 0 ,
$$
be a ...

**1**

vote

**3**answers

374 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 ...

**3**

votes

**1**answer

290 views

### Defining ideals for rational curves in space

A rational normal curve $C_d\subset\mathbb{P}^d$ is defined by quadrics. I guess, for the generic projection $\mathbb{P}^d\stackrel{\pi}{\to}\mathbb{P}^n$ the image $\pi(C_d)$ is still defined by ...

**4**

votes

**1**answer

297 views

### Minimal Free resolution of the ideals

What is the motivation to study the minimal free resolution of the ideals? Which geometrical information can we get from $res(I)$ for The variety of $I$?