# Tagged Questions

**8**

votes

**2**answers

407 views

### Proving that a generic variety with ample canonical bundle has no automorphisms

Let $X$ be a smooth projective connected variety over the complex numbers with ample canonical bundle. If $X$ is generic and $\dim X \leq1$, the automorphism group of $X$ is trivial, see for instance
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**0**

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**1**answer

188 views

### When is a cyclic cover hyperelliptic?

Let us work over the complex numbers for simplicity. Consider a curve $C$ presented as a cyclic cover of some lower genus curve $C'$. When $C'$ has genus $0$, we can write $C$ as the normalization of ...

**5**

votes

**4**answers

1k views

### The automorphism group of a hyperelliptic curve

Let $C$ be the projective smooth genus 2 curve defined by $y^2=x^5-x$ over $\mathbb F_5.$ What is the order of its automorphism group (automorphisms over $\mathbb F_5$)?
I have seen different ...