On the Number of Vedernikov–Ein Irreducible Components of the Moduli Space of Stable Rank 2 Bundles on the Projective Space

Abstract

We propose a method for finding the exact number of Vedernikov–Ein irreducible components of the first and second types in the moduli space M(0, n) of stable rank 2 bundles on the projective space P³ with Chern classes c₁ = 0 and c₂ = n ≥ 1. We give formulas for the number of Vedernikov–Ein components and find a criterion for their existence for arbitrary n ≥ 1.