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

Recently the paper by Hacon, McKernan and Xu appeared on the arXiv. There the authors prove that the number of birational automorphisms of a variety of general type can be bounded by using the volume of the variety itself. Moreover the authors claim to be able to use the same techniques, that appear in the paper, to prove Kollar's conjecture about DCC of the volumes (conjecture 1.4). I'd like to know if there are important applications of these statements, expecially consequences that follow directly from the boundedness of the automorphisms, regarding for example moduli of varieties. Thanks a lot.

share|cite|improve this question
Have you considered to contact the authors directly? – Martin Brandenburg Dec 2 '11 at 13:28

I don't have any direct/immediate consequence of the main result of the paper. However the techniques that we develop here are very useful. In work in progress, we plan to use these techniques to prove the boundedness of (semi) log canonical pairs (generalizing Alexeev's results do dimension \geq 3).

share|cite|improve this answer

Your Answer


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.