MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Let $X$ be a smooth projective variety over the complex numbers with trivial canonical bundle. Suppose that $X$ is Calabi-Yau.

Is the automorphism group of $X$ an arithmetic group?

What if $X$ is a K3 surface?

share|cite|improve this question
    
2  
I don't understand what information the previous comment is providing. But anyway, the answer for $K3$ surfaces is no. A counterexample, where the group is not even commensurable with an arithmetic group, was given by Totaro in Example 6.3 of this paper: math.ucla.edu/~totaro/papers/public_html/algebraic.pdf – potentially dense Feb 16 at 14:41
    
@potentiallydense Many thanks for your comment. That answers my question. Could you post your comment as an answer? – Christian Feb 16 at 15:05
up vote 7 down vote accepted

The answer for $K3$ surfaces is no. A counterexample, where the group is not even commensurable with an arithmetic group, was given by Totaro in Example 6.3 of this paper.

share|cite|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.