Today my kitten noticed my cursor moving around on my screen, and the moment I saw that tail wiggling, face swiveling back and forth following the cursor, I predicted a problem.
I figured that by asking for a solution early, before screen-scratching becomes a habit (I have brand new monitors, and the surfaces aren't glass!) I might avoid my expensive computer monitors being injured.
What can I do to dissuade my kitten from chasing my cursor arrow?
As a possible solution specific to the cursor issue, consider getting a monitor privacy screen (3M is a major manufacturer of such). This will limit the directions from which the screen, and thus the cursor, can be seen. This will remove the temptation since your cat will only see the cursor if she is looking directly at the monitor... meaning she's in your lap.
That said, I think in the long, it'll be a lot easier to train your cat to not jump up on the desk then to specifically not "go after the cursor". So I would focus training on that. There are plenty of articles, forum posts, and training guides on keeping a pet off of furniture. I personally favor the approach of rewarding for being on the floor rather than punishing for being on the furniture. There are some humane discouragement tools available if needed.
Also consider gating off the desk area so your cat cannot get close to the desk, let alone onto it. Or gate off the den/office if that is a possibility. Keep in mind wires are also very attractive to pets, especially young ones. Plus, since you can't be there 24/7, it'll keep her (I'm assuming gender here) away from the desk when you are not around. (It only takes a second for a pet to accidentally damage something.) As she gets older (since you refer to her as a kitten) or as you train her as to where she's allowed, you may not need the gated area.
