New results in geography and geometry of moduli spaces of stable rank 2 sheaves on projective space

In this talk, we will give an overview of recent results on the geography and geometry of the Gieseker-Maruyama
moduli scheme $M = M(c_1,c_2,c_3)$ of rank 2 stable coherent sheaves with first Chern class $c_1 = 0$ or $-1$,
second Chern class $c_2$, and third Chern class $c_3\ge0$ on the projective space $\mathbb{P}^3$.
We will enumerate all currently known irreducible components of $M$ for small values of $c_2$ and $c_3\ge0$.
We then present the constructions of new series of components of $M$ for arbitrary $c_2$. The problem of
connectedness of $M$ will be discussed. These are the resuts of several joint works of the speaker with
M.Jardim, D.Markushevich, A.Ivanov, C.Almeida and others.