Proposition 7.11(b) (Andreas Gathmann) The Segre embedding $f : \mathbb{P}^m \times \mathbb{P}^n \rightarrow f(\mathbb{P}^m \times \mathbb{P}^n) \subseteq \mathbb{P}^N$ is an isomorphism.
Is it an isomorphism of ringed spaces? How can I check? I showed the bijection. Link below:
http://www.mathematik.uni-kl.de/~gathmann/class/alggeom-2014/main.pdf
