1
$\begingroup$

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

$\endgroup$

0

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Browse other questions tagged or ask your own question.