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

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

2011-09-18

arxiv.org/abs/1109.3858v1

Mathematics

Algebraic Geometry

Preliminary version, comments welcome

Scientific paper

We consider an analogue of the notion of instanton bundles on the projective 3-space, consisting of a class of vector bundles defined on smooth Fano threefolds X of Picard number 1. We investigate their moduli spaces, focusing on non-emptiness, and, when the intermediate Jacobian of X is trivial, looking at the associated monads, hyper-determinants and nets of quadrics. We study one case where the intermediate Jacobian of X is non-trivial, namely when X is the intersection of two quadrics in the projective 5-space relating instanton bundles on X to vector bundles of higher rank on a curve of genus 2.

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