2011/09/18 by Daniele Faenzi, Faenzi, Daniele
Mathematics · #14F05 #14J60 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Meromorphic and Entire Functions #math.AG #msc:14F05 #msc:14J60
paper · pdf · doi:10.48550/arxiv.1109.3858
Updated and extended version. A study of jumping conics and nets of quadrics for prime Fano threefolds of genus 12 has been added
openalex publication_date 2011/09/18 · arxiv created 2013/04/10 · arxiv updated 2013/04/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 KX. 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.