Thank you. This is exactly the sort of statement I had hoped would be true. I have a couple of quick questions. 1. Since $a$ and $b$ should clear the denominators of $A$ for the argument to work, we could still expect the dimension of $V_{a,b}$ to be quite small even for arbitrarily big $a$ and $b$. Is that correct? 2. Does your argument use the fact that the volume is a limit rather than just a limsup? Thanks again.