Reflexive sheaf and ext sheaf

Question

Does there exist any result that characterize reflexive sheaves by the annulment of ext sheaf?

references on this subject are welcome!

Thanks a lot.

Answer 1

Here's a result that links reflexive sheaves with the codimension of related ext sheaves, from page 6 of The Geometry of Moduli Spaces of Sheaves by Huybrechts and Lehn:

Let $\mathcal{F}$ be a coherent sheaf of dimension $c$ on a smooth projective variety $X$. Then $\mathcal{F}$ is a reflexive sheaf if and only if $\mathrm{codim}(\mathcal{E}xt^q(\mathcal{F}, \omega_X)) \geq q + 2 $ for all $q > c$