Varieties without extra automorphisms II: hyperelliptic curves

For any field $k$ and integer $g \ge 2$, we construct a hyperelliptic curve $X$ over $k$ of genus $g$ such that $\#(\Aut X) =2$. We also prove the existence of principally polarized abelian varieties $(A,\theta)$ over $k$ of prescribed dimension $g \ge 1$ such that $\Aut(A,\theta)=\{\pm 1\}$.

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Published 1 January 2000