4
votes
1answer
136 views

Examples of hyperelliptic curves with hyperelliptic quotients that have more automorphisms

Does there exist a hyperelliptic curve $X$ of genus $g\geq 2$ over the complex numbers such that $X$ has a hyperelliptic quotient $X\to Y$ (in the sense that $Y$ is hyperelliptic and the morphism ...
8
votes
2answers
435 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 ...
3
votes
2answers
346 views

Automorphism group of a compact Kahler manifold

Good evening, I would like to ask the following questions. Let $X$ be a compact Kahler manifold. Denote by Aut(X) the group of all the biholomorphisms of $X.$ 1) What can we say about this group? ...
1
vote
1answer
199 views

On linear automorphism on positive definite matrices.

I saw a statement in [Murakami, On automorphisms on Siegel domains] that every linear automorphism $\phi$ on the set of positive definite matrices can be represented as conjugation: i.e. there is a ...