# 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, 𝜔 its canonical sheaf, and M the syzygy bundle of 𝜔. What is the degree of M?
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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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Given a finite dimensional algebra $A$ over a field $K$ with $\Omega^i(D(A)) \cong \Omega^{i+1}(D(A))$ for some $i \geq 1$, where $D(A)=\operatorname{Hom}_K(A,K)$. Do we then also have $\Omega^{-i}(A)... 3 votes 0 answers 77 views ### Normal set of points in the plane When defining the normality of a scheme in the book The Geometry of Syzygies, Eisenbud says that there are just a few facts that are known for their bounds. Given$X \subset \mathbb{P}^r$, we say ... 0 votes 1 answer 182 views ### Syzygies of projective varieties I want to see some examples of syzygies of projective varieties, if possible not from Eisenbud, because I know those. 2 votes 0 answers 145 views ### A question about an irreducible polynomial in the ideal of syzygies Let$G$be a finite group with$n$elements and let$\mathbb{Q}[x_1,\cdots,x_n]^G = \mathbb{Q}[g_1,\cdots,g_m]$, where$G$acts through the regular representation. Then there exist polynomials$s_j \... 522 views

### 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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### 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 ...
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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 ...
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 ...
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 $I$?