Why arkham city is stopping?

You're question is very vague. I will provide some possible answers.

1. It's the wrong resolution. Start the game launcher and set it to the resolution of the current screen, instead of starting the .exe directly

2. .exe is in the wrong folder.

3. .exe is out of date with the rest of the game.

4. The game is incompatible with your operating system.

5. Game is installed incorrectly. Try re-installing it.

If after reinstalling it the problem persists, the issue is probably with your computer and not the game.