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

Does anybody know any example of a semistable and nonsimple sheaf on a K3 surface $S$?

share|cite|improve this question
up vote 6 down vote accepted

The trival sheaf $\mathcal O_S\oplus\mathcal O_S$ is one: it has non-trivial global endomorphism algebra $gl_2(k)$ and is semi-stable.

share|cite|improve this answer
Are you sure it is semi-stable? – ginevra86 Feb 15 '11 at 14:28
Every line bundle is semistable, and a direct sum of semistable sheaves with the same slope is semistable with that slope. – Mattia Talpo Feb 15 '11 at 17:13

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.