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

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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 \({\mathbb{P}^5}\), relating instanton bundles on X to vector bundles of higher rank on a the curve of genus 2 naturally associated with X.

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  1. Université de Pau et des Pays de l’Adour, Avenue de l’Université, BP 576, 64012, Pau Cedex, France

    Daniele Faenzi

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  1. Daniele Faenzi
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Correspondence to Daniele Faenzi.

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Partially supported by ANR-09-JCJC-0097-0 INTERLOW and ANR GEOLMI ANR-11-BS03-0011.

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Faenzi, D. Even and odd instanton bundles on Fano threefolds of Picard number one. manuscripta math. 144, 199–239 (2014). https://doi.org/10.1007/s00229-013-0646-6

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