Full Idea
It's robustly part of common sense that fictional objects don't exist in any sense at all, and this means they aren't abstracta either.
Gist of Idea
If fictional objects really don't exist, then they aren't abstract objects
Source
Jody Azzouni (Deflating Existential Consequence [2004], Ch.3)
Book Reference
Azzouni,Jody: 'Deflating Existential Consequence' [OUP 2004], p.72
A Reaction
Nice. It is so easy to have some philosopher dilute and equivocate over the word 'object' until you find yourself committed to all sorts of daft things as somehow having objectual existence. We can discuss things which don't exist in any way at all.