On the Moduli Space of Coherent Systems of Type (2, c₁, c₂, 2) on Projective Plane

We study the moduli space of coherent systems in P² using the Segre invariant. We obtain necessary conditions for the existence of -semistable coherent systems (E, V) of type (2, c₁, c₂, k), with k 2. Afterwards, we give numerical conditions to the nonemptiness of the moduli space and compute the critical values depending of the Chern classes. Finally, we give some topological properties of the flips.