Instanton Sheaves on Ruled Fano 3-folds of Picard Rank 2 and Index 1

Abstract

We study rank 2 $h$-instanton sheaves on projective threefolds. We demonstrate that any orientable rank 2, non-locally free $h$-instanton sheaf with defect 0 on a threefold can be obtained as an elementary transformation of a locally free $h$-instanton sheaf. Our focus then shifts to ruled Fano threefolds of Picard rank 2 and index 1, of which there are five deformation classes. We establish the existence of orientable rank 2 $h$-instanton bundles on such varieties. Additionally, we prove the existence of Ulrich bundles on such varieties, which correspond to $h$-instanton sheaves of minimum charge.

21 pages, comments welcome!

References in corpus (2)

• Instanton bundles on the blow up of the projective $3$-space at a point
• Even and odd instanton bundles on Fano threefolds