Symmetric powers and a problem of Kollar and Larsen
arXiv:0810.0853 · doi:10.1007/s00222-008-0140-z
Abstract
We prove a conjecture of Kollar and Larsen on Zariski closed subgroups of $GL(V)$ which act irreducibly on some symmetric power $Sym^{k}(V)$ with $k \geq 4$. This conjecture has interesting implications, in particular on the holonomy group of a stable vector bundle on a smooth projective variety, as shown by the recent work of Balaji and Kollar.
49 pages. Inventiones Mathematicae, to appear