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2
votes
1answer
328 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
3answers
332 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
1answer
267 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
1answer
283 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 $I$?