Harder-Narasimhan filtration of rank 4 vector bundles on $P^2$ - MathOverflow most recent 30 from http://mathoverflow.net2013-05-25T20:19:32Zhttp://mathoverflow.net/feeds/question/58722http://www.creativecommons.org/licenses/by-nc/2.5/rdfhttp://mathoverflow.net/questions/58722/harder-narasimhan-filtration-of-rank-4-vector-bundles-on-p2Harder-Narasimhan filtration of rank 4 vector bundles on $P^2$ Alexandra Seceleanu2011-03-17T05:14:56Z2011-03-18T01:46:45Z
<p>Given a non-semistable vector bundle on $P^2$ of rank 4, are explicit conditions known for when the ranks in its Harder-Narasimhan filtration are (3,1), (2,2) and (1,3) respectively? </p>
<p>I would be very happy, if this is worked out somewhere, to be pointed to a reference.</p>
<p>I can see the resemblance of my question to <a href="http://mathoverflow.net/questions/53883/moduli-space-of-vector-bundles-with-fixed-harder-narasimhan-filtration" rel="nofollow">this other question on moduli spaces of vector bundles with fixed HN filtration factors</a>, but I am hoping something more concrete is known, perhaps in the low rank situations. </p>