# Questions tagged [syzygies]

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

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### Degree of the syzygy bundle of a curve of genus 3

Let X be an hyperelliptic curve of genus 3, đťś” its canonical sheaf, and M the syzygy bundle of đťś”. What is the degree of M?
• 237
3 votes
1 answer
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### Hilbert's Syzygy Theorem in the bigraded case

I've been recently wondering how to prove the existence of a Hilbert polynomial for finitely generated bigraded modules $M$ over a polynomial ring $R=k[X_0,...,X_n,Y_0,...,Y_m]$ with the usual ...
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### Identities satisfied by the image of the Young symmetrizer

Consider a partition $\lambda=(r_1,\ldots,r_k)$ of an integer $n$ and the corresponding Young diagram with rows of length $r_1,\ldots,r_k$ (hence ordered in non-increasing order). Counting the column ...
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2 votes
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### Castelnuovo Mumford Regularity

Consider the polynomial ring $S = C[x_1,\ldots,x_n]$. Let $$â€Žâ€Ź0 â€Žâ€Ž\rightarrowâ€Žâ€Žâ€Ź â€ŽE_{n-1} â€Žâ€Ž\rightarrow â€Ž\cdots â€Žâ€Žâ€Ž\rightarrow â€ŽE_1 â€Žâ€Žâ€Ž\rightarrow â€ŽE_0 \rightarrow I \rightarrow 0â€Ž â€Ž,â€Ž$$ be a ...
• 73
1 vote
3 answers
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### 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 ...
• 4,692
3 votes
1 answer
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### 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 ...
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4 votes
1 answer
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### 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 $I$?