# Sheaf ext of locally free sheaves

Let $$E$$ be a locally free sheaf of rank $$>1$$ over a smooth projective variety. Then what is $$\mathcal{E}xt^1(E,O_X)$$? If it's a line bundle, I know that is zero.

Is this $$H^1(\mathcal{H}om(E,O_X))$$?

• Your notation suggests you want sheaf ext, in which case it is zero. The second paragraph suggests global ext, in which case it may not be zero. – Mohan Jun 17 at 13:48
• I want sheaf ext only. Thanks for letting me know that it's zero. – user52991 Jun 17 at 13:54