I have a new iMac / Catalina. I can not open my Aperture. What to do?

Aperture was discontinued 5 years ago. It is no longer developed or sold. It was replaced by the less capable (but free) Photos.app that comes with the OS. You can migrate to that app very simply:

Hold down the option (or alt) key and launch Photos. From the resulting menu select 'Choose Library' and point at your Aperture Library. It will do the rest.

If you prefer not to use Photos there are several 3rd party apps that you can use. Which to choose depends on the kind of photographer you are and your budget.

Aperture can't be run in Catalina. Launch Photos with the Option key held down and choose its library, or use a non-Apple alternative.

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Or search on Github for Retroactive. It is a tool which will restore many functions of Aperture on Catalina.

Be aware of two things with Retroactive: not all features of Aperture work under it and there are numerous reports of system instability from folks who've used it. Aperture is dead 5 years. It's long past time to move on.