Irreducibility of the moduli space of orthogonal instanton bundles on ℙⁿ

2018/03/29 by Andrade, Aline V., Marchesi, Simone, Miró-Roig, Rosa Maria
#14D20 #14J60 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1803.11237

Abstract

In order to obtain existence criteria for orthogonal instanton bundles on ℙn, we provide a bijection between equivalence classes of orthogonal instanton bundles with no global sections and symmetric forms. Using such correspondence we are able to provide explicit examples of orthogonal instanton bundles with no global sections on ℙn and prove that every orthogonal instanton bundle with no global sections on ℙn and charge c≥ 3 has rank r≤ (n-1)c. We also prove that when the rank r of the bundles reaches the upper bound, MℙnO(c,r), the coarse moduli space of orthogonal instanton bundles with no global sections on ℙn, with charge c≥ 3 and rank r, is affine, reduced and irreducible. Last, we construct Kronecker modules to determine the splitting type of the bundles in MℙnO(c,r), whenever is non-empty.

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