A special D4-D2-branes configuration on K3 fiberation Calabi-Yau threefolds

We construct a special D4-D2-brane configuration on the K3 fibered Calabi-Yau threefolds: canonical D4-branes on K3 fiberations and another D2-branes on its base ${\mathbb{P}}_1$, by using the ordinary nonlinear sigma model in two dimensions. We would derive the exact expression of $Ext$ groups of this construction. By using the Gepner model, we achieve the feasibility of the existence of such a configuration and get more available sheaf’s data of this brane system.