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arXiv · 0810.0853

Symmetric powers and a problem of Kollar and Larsen

Robert M. Guralnick·Pham Huu Tiep
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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.

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Robert M. Guralnick, Pham Huu Tiep. 2008-10-05. Symmetric powers and a problem of Kollar and Larsen. https://doi.org/10.1007/s00222-008-0140-z

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