# why Kontsevich-Soibelman stability condition is a generalization of stable bundle condition

Just as the title, I head from a lecture. Could any body explain this in a detailed way? Thanks.

Central charge is defined on page20 of 0811.2435, which I think comes from physical definition of central charge: as a linear map from weigth lattic to complex plane, satisfy some stability condition.

stable bundle is defined as in wiki: http://en.wikipedia.org/wiki/Stable_vector_bundle

• in a more concrete way: why deg(E)/rank(E) of a vector bundle E satisfy definition of central charged defined by KS. May 10, 2011 at 15:37
• It would be nice if you would write out the definition of a central charge, or at least link to it. May 10, 2011 at 16:39
• I'd say you should include as much detail in your question as you would hope for in an answer. (You can edit your question.) May 10, 2011 at 16:43
• Kontsevich-Soibelman stability is a modified version of Bridgeland stability. A good survey for Bridgeland stability and how its related to $\mu$-stability (usually attributed to Mumford not to Hitchin) can be found in Bridgelands overview article "spaces of stability conditions" math.AG/0611510. May 11, 2011 at 9:56