Some new components of the moduli scheme $\mathrm M_{\mathbb P^3}(2;-1,2,0)$ of stable coherent torsion free sheaves of rank 2 on $\mathbb P^3$

M. A. Zavodсhikov

Yaroslavl State Pedagogical University named after K. D. Ushinsky

Abstract: In this paper we consider Giseker–Maruyama moduli scheme $\mathrm M:=\mathrm M_{\mathbb P^3}(2;-1,2,0)$ of stable coherent torsion free sheaves of rank 2 with Chern classes $c_1=-1$, $c_2=2$, $c_3=0$ on 3-dimensional projective space $\mathbb P ^3$. We will define two sets of sheaves $\mathcal M_1$ and $\mathcal M_2$ in $\mathrm M$ and we will prove that closures of $\mathcal M_1$ and $\mathcal M_2$ in $\mathrm M$ are irreducible components of dimensions 15 and 19, accordingly.

Keywords: compactification, moduli scheme, coherent torsion free sheave of rank 2, 3-dimensional projective space.

UDC: 512.723

Received: 21.06.2011