Even and odd instanton bundles on Fano threefolds of Picard number 1

Abstract

We consider an analogue of the notion of instanton bundle on the projective 3-space, consisting of a class of rank-2 vector bundles defined on smooth Fano threefolds X of Picard number one, having even or odd determinant according to the parity of K_X. We first construct a well-behaved irreducible component of their moduli spaces. Then, when the intermediate Jacobian of X is trivial, we look at the associated monads, hyperdeterminants and nets of quadrics. We also study one case where the intermediate Jacobian of X is non-trivial, namely when X is the intersection of two quadrics in P5, relating instanton bundles on X to vector bundles of higher rank on a the curve of genus 2 naturally associated with X.

Updated and extended version. A study of jumping conics and nets of quadrics for prime Fano threefolds of genus 12 has been added

References in corpus (3)

• Semiorthogonal decomposition for algebraic varieties
• The Abel-Jacobi map of a moduli component of vector bundles on the cubic threefold
• Instanton bundles on Fano threefolds

Cited by in corpus (5)

• Instanton bundles on Fano threefolds
• Globally generated vector bundles of rank 2 on a smooth quadric threefold
• Compactification of the moduli space of instanton sheaves on the Fano threefold $V_5$
• A refined stable restriction theorem for vector bundles on quadric threefolds
• Torsion free instanton sheaves on the blow-up of ${\mathbb{P}}^3$ at a point