A Class Of Rank 2 And 3 Donaldson-Thomas Invariants

In this paper we want to report the full theory of Donaldson-Thomas in-variants which is a phenomenon happened on the Calabi-Yau 3-folds. Firstly the preliminaries of Donaldson-Thomas theory are introduced and then a detailed computation of rank-2 Donaldson-Thomas invariant is presented. Following the rank-2 case, we study the case when the rank goes up to 3 and give some pre-liminary results on the stabilities of vector bundles. Based on these results, we construct rank-3 stable bundles on P1×Pn. At last, the relations between Donaldson-Thomas invariants and Gromov-Witten invariants, as well as the new development of Donaldson-Thomas invariants are discussed, which might shed some light on our future research work.