A notion of Δ-multigenus for certain rank two ample vector bundles

Abstract

A notion of "delta-genus" for ample vector bundles $\mathcal{E}$ of rank two on a smooth projective threefold X is defined as a couple of integers (δ₁, δ₂). This extends the classical definition holding for ample line bundles. Then pairs (X, $\mathcal{E}$) with low δ₁ and δ₂ are classified under suitable additional assumptions on $\mathcal{E}$.