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# Mathematical Research Letters

## Volume 7 (2000)

### Number 1

### Varieties without extra automorphisms II: hyperelliptic curves

Pages: 77 – 82

DOI: http://dx.doi.org/10.4310/MRL.2000.v7.n1.a7

#### Author

#### Abstract

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 $\Aut(A,\theta)=\{\pm 1\}$.