@mastersthesis {2013, title = {Semistability and Decorated Bundles}, year = {2013}, school = {SISSA}, abstract = {This thesis is devoted to the study of semistability condition of type t=(a,b,c,N) decorated bundles and sheaves in order to better understand and simplify it. We approach the problem in two different ways: on one side we {\textquotedblleft}enclose{\textquotedblright} the above semistability condition between a stronger semistability condition (\epsilon-semistability) and a weaker one (k-semistability), on the other side we try, and succeed for the case of a = 2, to bound the length of weighted filtrations on which one checks the semistability condition.}, keywords = {Decorated sheaves, semistability, moduli space, Mehta-Ramanathan, maximal destabilizing subsheaf}, url = {http://hdl.handle.net/1963/7130}, author = {Andrea Pustetto} }