Mathematical Research Letters

Volume 7, Issue 1, January 2000 pp. 77-82.

Varieties without extra automorphisms II: hyperelliptic curves

Authors: Bjorn Poonen
Author institution: University of California, Berkeley

Summary: 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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