On automorphisms of Hilbert squares of smooth hypersurfaces

Abstract

Let $X$ be a smooth projective hypersurface of dimension at least three. We show that every automorphism of the Hilbert square $X^{[2]}$ of $X$ is induced by some automorphism of $X$.

v3: Minor changes, final version. v2: 11 pages. Result strengthened according to J. V. Rennemo's suggestion