I am trying to prove that the twisted cubic $C: (u,v)\rightarrow(u^3,u^2v,uv^2,v^3)$ has as resolution $$ 0\rightarrow \mathcal O(-1)^2\rightarrow \mathcal O^3\rightarrow \mathcal I_C(2)\rightarrow0, $$ where $\mathcal I_C$ is the ideal sheaf, using the Beilinson Theorem.
For this I must calculate the cohomology $H^i(\Omega^j(j)\otimes\mathcal I_C(2))$ (actually I only need the dimension), but I do not now how compute that, any tips of methods or literature that can help me?
Thanks in advance.