We investigate the logarithmic bundles associated to arrangements of hypersurfaces with a fixed degree in a smooth projective variety. We then specialize to the case when the variety is a quadric hypersurface and a multiprojective space to prove a Torelli type theorem in some cases.

No abstract

A del Pezzo threefold F with maximal Picard number is isomorphic to P 1 ×P 1 ×P 1 . In the present paper we completely classify locally free sheaves E of rank 2 such that h i F, E(t) = 0 for i = 1, 2 and t ∈ Z. Such a classification extends similar results proved by E. Arrondo and L. Costa regarding del Pezzo threefolds with Picard number 1.

International audienceWe provide two examples of smooth projective surfaces of tame CM type, by showing that the parameter space of isomorphism classes of indecomposable ACM bundles with fixed rank and determinant on a rational quartic scroll in IP5 is either a single point or a projective line. These turn out to be the only smooth projective ACM varieties of tame CM type besides elliptic curves, [1]. For surfaces of minimal degree and wild CM type, we classify rigid Ulrich bundles as Fibonacci extensions. For IF0 and IF1, embedded as quintic or sextic scrolls, a complete classification of rigid ACM bundles is given

Abstract. We investigate the existence of globally generated vector bundles of rank 2 with c1 ≤ 3 on a smooth quadric threefold and determine their Chern classes. As an automatic consequence, every rank 2 globally generated vector bundle on Q with c1 = 3 is an odd instanton up to twist.