On the Moduli Space of Coherent Systems of Type $(2,c_1,c_2,2)$ on Projective Plane

Abstract

We study the moduli space of coherent systems in $P^2$ using the Segre invariant. We obtain necessary conditions for the existence of $\alpha$-semistable coherent systems $(E,V)$ of type $(2,c_1,c_2,k)$, with $k\ge 2$. 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.

arXiv comment30 pages, no figures