Hi, I have an iMac 2013 can I install Big Sur on this machine?

dialabrain is 100% correct. You can run Catalina 10.15.7, Apple has a history of supporting legacy versions of Mac OS for several years, my guess is at least 3 more years. There is a fair chance you will want to upgrade the 2013 within the next 2-3 years anyhow.

No. 2014 or later iMac required.

You're welcome.

Your welcome.