On the rationality of the moduli space of instanton bundles on the projective 3-space

2018/05/16 by Halic, Mihai, Tajarod, Roshan
#14D20 #14D21 #14J60 #14M20 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1805.06414

Abstract

We prove the rationality and irreducibility of the moduli space of---what we call---the endomorphism-general instanton vector bundles of arbitrary rank on the projective space. In particular, we deduce the rationality of the moduli spaces of rank-two mathematical instantons. This problem was first studied by Hartshorne, Hirschowitz-Narasimhan in the late 1970s, and it has been reiterated within the framework of the ICM 2018.

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