Hisato Matsukawa

Weighted configurations and the nonexistence of arithmetic ball quotient compactifications

We prove that, for every $n\ge9$, no ordered GIT quotient of $n$ points on $\mathbb P^1$ with positive rational weights smaller than one and of total weight two is isomorphic to the Baily--Borel compactification of an arithmetic complex ball quotient. The weights may lie on stability walls, and the lattice may have tor...