Construction of stable rank 2 sheaves on projective space

We study the moduli space M(e,n,m) of semi-stable rank 2 coherent sheaves on the projective space P^3 with first Chern class e=0 or -1, positive second Chern class n, and nonnegative third Chern class m. We are also interested in the subspace B(e,n) of M(e,n,0) which is the moduli space of rank 2 stable vector bundles on P^3. We show that, for e=-1 and any possible values of n the space M(-1,n,0) contains at least one rational irreducible component, and for both e=0 and e=-1, arbitrary n, and m varying in a big range, M(e,n,m) contains rational irreducible components. We also provide new big series of irreducible components of B(e,n). These are the results of our joint works with C. Almeida and M. Jardim, and with D. Vassiliev.