Let $C\subset\Bbb{P}^n$ be an ACM (arithmetically Cohen-Macaulay) curve with homogeneous coordinate ring $R$. Then there is an exact sequence

 

$$0\to \text{Tor}_i(R,\Bbb{C})_k\to H^1(C,\wedge^{i+1}M_L(k-i-1))\to H^1(C,\wedge^{i+1}\Gamma(k-i-1))\to H^1(C,\wedge^i M)L(k-i))\to 0$$

 

Where $\Gamma$ is trvial of rank $n+1$ and and $M_L$ is the kernel of the surjection $\Gamma(C,\mathcal{O}_C(1))\to \mathcal{O}_C(1)$

Can someone please suggest a reference for this fact? I cannot find it anywhere

Let $C\subset\Bbb{P}^n$ be an ACM (arithmetically Cohen-Macaulay) curve with homogeneous coordinate ring $R$. Then there is an exact sequence

$$0\to \text{Tor}_i(R,\Bbb{C})_k\to H^1(C,\wedge^{i+1}M_L(k-i-1))\to H^1(C,\wedge^{i+1}\Gamma(k-i-1))\to H^1(C,\wedge^i M)L(k-i))\to 0$$

Where $\Gamma$ is trvial of rank $n+1$ and and $M_L$ is the kernel of the surjection $\Gamma(C,\mathcal{O}_C(1))\to \mathcal{O}_C(1)$

Can someone please suggest a reference for this fact? I cannot find it anywhere